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GitHub Universe Meets New Goals, Doesn't Lose Wow Factor
Author: Nichole Bernier
Attendees at GitHub Universe soak up the tech and the venue — the Palace of Fine Arts, the only structure standing from San Francisco's 1915 Exposition. (Photos courtesy GitHub)
Web hosting company GitHub launched its first conference for software developers in 2015 at San Francisco's Pier 70. It was a good fit — the venue's raw, industrial atmosphere underscored the company's funky DIY vibe — and the company brought GitHub Universe back to Pier 70 for its 2016 and 2017 editions. But in 2018, the venue was in the throes of a multi-use project redevelopment and unavailable over GitHub Universe's dates, Oct. 16–17.
Hosting the event in a new venue was among a number of new moves that GitHub needed to make for its fourth conference. The tech company had a new goal of increasing conference revenue without physically growing the event much beyond its 1,700 attendees, for fear of sacrificing its intimate atmosphere. Then, there was the small matter that GitHub had just been bought by Microsoft in June for a cool $7.5 billion — and wanted all the optics to convey that it was still the same edgy, personal, and inclusive community it had always been.
When the company's event producers tried to figure out how to manage it all —increasing profits but not size, while conceptualizing a new venue, and keeping it real — they decided they needed help. They reached out for RFPs from event agencies with a reputation for innovative work.
"One of my colleagues who manages sponsorship had visited [Intuit's] QuickBooks Connect conference in San Jose and was very impressed by the quality of production put on by its coordinator, Agency EA," said Kelsey Schimmelman, GitHub's senior event producer. "So when we put Universe 2018 up for RFP, we submitted it to them." In addition to Intuit, Agency EA has worked with Google, Oprah Winfrey, and the Obama Foundation. "Their pitch impressed us so much," Schimmelman said, "that we switched from our incumbent vendor."
The landmark Palace of Fine Arts provides GitHub with a blank canvas for activation and engagement.
Festival Space
GitHub's goal is to outdo itself, year after year, while continuing to prioritize the needs of every attendee. The challenge for Agency EA was not just changing locations, but finding a location that could support a festival ambience scaled down for intimacy and creating a space that would enable them to woo more sponsors more substantively and lucratively.
Given GitHub's preference to stay in San Francisco, Agency EA eyed a historic city landmark with a World Fair pedigree: The Palace of Fine Arts. The only structure still standing from San Francisco's 1915 Exposition, the Palace is a tall drink of water, from its dramatic Greek-style colonnades to its soaring central rotunda. (Unsurprisingly, its exterior is also an extraordinarily popular wedding-photo backdrop, a reality any event there must cheerfully contend with.) The interior is a high-ceiling space like an airplane hangar, a tabula rasa for creativity.
"It was beautiful, and so much fun to create an almost shocking juxtaposition of this classical, stunning architectural style on the outside," Schimmelman said, and creating a playground for attendees with "a super high-tech, colorful, well-lit interior."
A statement location like this with flexible space gave GitHub the freedom to put up walls to reconfigure the square footage. But with that flexibility and creativity comes a certain amount of unpredictability.
"The venue was a great fit for the client, kind of quirky and unique like their brand is," said Kristin Barbour, account director at Agency EA. "They typically like non-trade venues, and are conscious of not turning into your typical conference. They never aspire to be a Moscone event. But it's a raw space so we knew we'd have to get creative with space blocking. The floor space is a challenge, and the configuration can change by the week, depending on what was done by a previous client." Indeed, when Barbour and her colleagues visited the space two weeks before the conference, they found that there was an entirely new room in the space where they'd planned to place tech tables.
Agency EA addressed the nontraditional space and need for breakouts by building a 360-degree open stage for the general session, which could be divided into three triangular spaces curtained off for smaller stage events. The lighting was likewise divisible: A large, circular, overhead LED deck had a custom triangular divider nesting inside, and it could be lowered in pieces for the needs of the subdivided stage in-the-round.
"It's a totally different experience for general sessions when you use a 360-degree stage. You get up close and personal with the speakers," Barbour said. "It's all visible, all accessible, with less attention to what the walls are than the freedom of what you want to do in the total space."
The Palace of Fine Arts' classical exterior stands in striking juxtaposition to GitHub Universe's creative use of indoor spaces.
When she says accessible, she doesn't just mean it figuratively. To maximize the acoustics and minimize sound bleeding from one subdivided stage to another, an under-seat audio system was installed, with speakers wired under the chairs to keep the sound experience hyper local. The sessions were also fully closed-captioned, useful not only for the hearing-impaired (there was an ASL interpreter on hand) but for the large number of livestream viewers — 250,000 remote viewers over the two days of the show — who might be watching in an environment with the volume down.
"GitHub knows they have a broad customer base of code developers all over the world, and they want to make sure everyone could have the same experience at the event," Barbour said.
Accommodating the needs of the hearing-impaired was one of a number of GitHub's initiatives to take care all of their attendees and to ensure that they all felt welcome. "It was important to have full inclusivity features," Barbour said. GitHub "set the foundation, and our team ran with it. They traditionally have a meditation room, just a quiet place to go, but we made sure it also had prayer rugs and ambience lighting. Same thing for the parents' room, a little place where we brought in children's books and nursing stations so multiple parents could be in there at the same time."
The event was fully ADA accessible, and as comfortable for mothers with babies as for attendees with service dogs. Restrooms were gender neutral. Gift-shop swag included GitHub logo onesies for the littlest future coders, as well as trans and pride T-shirts, and preferred pronoun stickers for name badges. Service animals were welcome on the conference floor, and accommodated with a pet relief area and treats.
A scholarship program enabled people to attend the conference — students and people from marginalized communities — who otherwise might not have the means to register. "This accessibility is something we've always done. It's a core part of our event values," Schimmelman said. "These are some of the people who do the most interesting work on GitHub, and it's important that they be there."
A tunnel entryway that changed colors is another example of how organizers of GitHub Universe 2018 used experiential design whenever they could.
Sponsor Customization
The individualized attention extended as thoroughly to the sponsors. At Universe 2018, they were assured the sponsorship experience wouldn't be about cookie-cutter rental structures, logos slapped on walls, and typical giveaway tchotchkes. Everything was customized for each sponsor.
"There were 30 sponsors across several different tiers, requiring a capacity of customization and level of detail we had never really done before," said Angelina Spaniolo, senior creative strategist for Agency EA. Logos and brand representations would be more abstract, so rather than a chaotic branding experience, attendees walked through a gallery environment — with curated décor, texture, and lighting. "Each sponsor had their own art installation and we worked deeply with them, bringing to life a buildout to showcase their brand in a special light," Spaniolo said.
GitHub is an open-source community, after all, and that individuality is a big part of who they're bringing to the platform. Having an attention-catching way of presenting who these sponsors are — and what they could do for developers — was very important to Universe 2018. "It was all custom-built. With sponsors, you are on tight budgets, and trying to figure out creative budget-conscious installations," Spaniolo said. "We had graphic designers and fabrication partners helping us see all these through from a build perspective."
The installations and price points varied by footprint size, function, and add-on services. An 8-by-8-foot footprint focused on something visually compelling, a photo-op stop. A 10-by-10-foot space was designed to be an interactive hangout, and a 20-by-30-foot area was a sort of developer lounge, meant for relaxation and interaction. Sponsorship packages included options for interactive components and demo stations, and the customization was virtually limitless. One sponsor with ship references in its branding story was represented with a live aquarium, filled with fish genetically modified to glow under black light. Another had a 10-foot-high, glow-in-the-dark Kraken sea monster on a giant pedestal, while elsewhere in the room, another sponsor had a large remote-controlled excavator in a sandbox.
One sponsor of GitHub Universe was represented with a 10-foot-high, glow-in-the-dark Kraken sea monster on a giant pedestal.
Room to Play
But in the end it wasn't only about the wow factor: Attendees had to know beyond a shadow of a doubt that they were at a GitHub event. And that's where the role of whimsy comes in.
"I think our community is really great in terms of the way they embrace play. A lot of developers have a child-like wonder and openness to approach things with a sense of new eyes," Shimmelman said. "When you're in that state of mind, you're in this great head space to make new connections and friends, and that's a great way for people to network. I like anything that encourages attendees to play. I knew immediately that the adult playroom would be a hit."
Yes, adult playroom. One sponsor decided to bring a children's play space alive for adults, including a 10-foot-high teddy bear and life-size rocking horse. Coloring vinyls were available on highboys for spontaneous arts & crafts. And a giant toy box glowed yellow from within, emanating angelic noises and filled with branded giveaway items that would appeal to children.
GitHub provided some of its own interactive whimsy with an Octocat (its mascot) Generator Lounge, where attendees could make their own custom avatars at kiosks, adding hair and clothing to the cult-star Octocat. "People walked away feeling they had their own little piece of the GitHub brand," Schimmelman said. "We're lucky our community is willing to do so much evangelizing. We really have fans rather than users, and we try to respect that."
The proof of the event's success was evident in the way it hit its markers: positive feedback from attendees and sponsors, and a solid revenue increase. "We had explicit revenue goals, and tripled the sponsorship — both in terms of the number of sponsors and the amount of revenue," Schimmelman said. "I think marketing people at the conference recognize the value of an art-installation sponsorship in terms of the social-media attention it can generate."
Many sponsors are accountable to executives back home, and expected to return with an Excel spreadsheet of all the cards they collected. But GitHub stresses a quality-over-quantity mentality, reflected in a comment from sponsor GitKraken on GitHub's website: "We know we can count on having real conversations with people at GitHub events, and that attendees aren't just visiting booths to get free stuff. GitHub strives to build an interactive environment for both sponsors and attendees, which creates real value."
Amid the shiny objects there was real substance. The conference layout in the Palace included a gallery space to showcase the life and work of people doing interesting things using GitHub. There was a Detroit water project, in which a woman created a community platform to help donate to the water bills of people struggling to get clean water. And there was an organization that helps military vets learn to code so they can launch their careers post-deployment.
"GitHub is [about] business, but it's people over technology," Schimmelman said. "Technology is the landscape we all live in. But people are the subject of the stories we tell."
Nichole Bernier is a writer and editor based in Massachusetts.
Programmed Fun at GitHub Universe
The focus on interactivity and conversation extended to leisure time during GitHub Universe. Social events were designed for maximum engagement and sensitivity to the audience of developers and coders, many of whom skew toward introversion. As such, GitHub's Kelsey Schimmelman didn't want to make the concluding after-party a sensory overload of dancing and loud music.
So 2018's after-party tapped attendees' innate curiosity for technology with a DJ who coded: As he spun the tunes, live code was manipulated and projected on a screen behind him, a technical visual representation of the music he played.
"People were standing around staring, and saying to each other, 'Wow, that's amazing,'" Schimmelman said. "It was another conversation piece for people to connect."
Sponsorship packages at GitHub Universe 2018 included options for interactive components and demo stations, and the customization was virtually limitless.
GitHub Universe's spaces played up the creative side of its brand, including a meditation room with a lot of extras.
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Sherrif Karamat, President and Chief Executive Officer
Sherrif Karamat, CAE, is President and Chief Executive Officer of PCMA. Karamat also serves as President of the PCMA Foundation and Publisher of Convene magazine.
As CEO, Karamat leads the vision, mission and promise for PCMA's global family of brands. Karamat serves the greater business events industry as a prominent business architect, enabling our community to become a catalyst for economic and social progress, organizational success, and personal and professional development.
In his previous role as Chief Operating Officer, Karamat led the development and implementation of PCMA's new vision: driving global economic and social transformation through business events. In addition to his responsibilities at executive level, Karamat also directed streamlining of PCMA's content creation and delivery channels into one organization. He oversaw partnership, business services, membership, business development and technology teams.
As part of PCMA's growth strategy, Karamat has led a major data intelligence program and played a key role in the 2017 acquisition of Incentive Conference & Event Society Asia Pacific (ICESAP).
A leader in the business events industry, Karamat previously served as Vice President of Business Sales and Services for Toronto Convention & Visitors (Tourism Toronto). He has served on various boards and is currently a director on the Destination International Board of Trustees.
Karamat is a life-long learner. In addition to completing his bachelor's degree and Masters of Business Administration from York University in Toronto, Canada, he has completed postgraduate certificate programs at Wharton School of Business at University of Pennsylvania, Kellogg School of Management at Northwestern University and the University of Chicago. At Harvard Business and Law School, he completed a program on strategic negotiations for senior executives and a program at Massachusetts Institute of Technology (MIT), one on data intelligence and big data.
Robert Haas, Chief Administrative Officer
Robert Haas is responsible for PCMA's IT, human resources, data and finance departments as its first Chief Administrative Officer. He utilizes data, content and personalized experiences to help PCMA better understand its members' needs and develop an audience-focused strategy.
Haas has more than 15 years of database marketing, product development and consulting experience from working in business-to-business and business-to-consumer industries. He understands how innovation, research and technology intersect and evaluates what is leading edge versus cutting edge.
Haas will leverage data to determine best practices in business events and how the industry can drive global economic and social transformation.
He previously served as PCMA's Chief Innovation Officer. He joined PCMA as Vice President of Business Development and Data Intelligence. His previous roles include Senior Vice President of Strategic Product Development and Marketing at Scranton Gillette Communications Inc. and in direct response marketing for Tribune Direct.
He has a bachelor's degree in international business from St. Norbert College in De Pere, Wisconsin.
Mona Cotton, Chief Business Officer
As Chief Business Officer, Mona Cotton leads the Business Development, Client and Member Services, and Business Services teams. She has more than 20 years of business leadership experience in the areas of partnership, sponsorship, business development, media publishing and business services.
Cotton, a PCMA leader for more than 15 years, takes a strategic approach to transforming PCMA's client relationships and business opportunities. Her role at PCMA is to facilitate connections between business-to-business organizations and business-to-consumer operations, identifying opportunities to fuel economic and social progress and success for PCMA and its members, customers and clients.
While she has watched as business events shifted from logistics to engagement, Cotton said the value of relationships remains steadfast in the industry.
Prior to PCMA, Cotton led and supported various sales efforts at the National Association of REALTORS, Airborne Express (now DHL) and Fox Associates, a Chicago-based magazine representative firm. She received a bachelor's degree in marketing and advertising from Indiana University.
Michelle Crowley, Chief Growth & Innovation Officer
Michelle Crowley oversees regional brand development, content outreach and innovation as PCMA's first Chief Growth & Innovation Officer. She is responsible for regional and revenue development in the Americas, Asia Pacific (APAC) and Europe, Middle East and Africa (EMEA) regions. In addition, Crowley is responsible for education and product development.
She leads PCMA's global growth strategy by evaluating and identifying how the organization can deliver value to its members through new and existing business models, education programs and new products.
Crowley began her career at PCMA and continues to work with global travel brands, build strategic relationships and partnerships with key markets, and design year-round engagement campaigns. She has held various positions at PCMA including Vice President for Global Growth and Business Transformation.
Crowley is 2019 MBA graduate of the Kellogg School of Management at Northwestern University. She received her bachelor's degree from University of Illinois at Urbana-Champaign.
Meredith Rollins, Chief Community Officer
As PCMA's first Chief Community Officer, Meredith Rollins leads the community engagement team.
The team delivers programs and services that strengthen the connections between PCMA members, facilitate knowledge sharing and advance the network of professionals in the global business events industry. Her key areas of responsibility include community and chapter engagement, research, social impact and volunteerism. She remains Executive Director of the PCMA Foundation.
Rollins joined PCMA in 2007 and held roles in project management, global development and account management with the PCMA partnership program. She was Director of Strategic Development for the Association for Corporate Growth, a global community for middle-market M&A business leaders from 2012 to 2015. Rollins became Executive Director of the PCMA Foundation in 2015.
Rollins received a bachelor's degree in business administration from the University of Illinois at Urbana-Champaign and an MBA from Northwestern University's Kellogg School of Management.
Gina Meier, Director, Human Resources
Gina Meier is Director of Human Resources for PCMA, a position she has held since 2006. She is responsible for helping PCMA execute its vision of driving global economic and social transformation through its human capital.
Her responsibilities including professional development, culture, talent development, employee integration and employee engagement.
Meier began her human resources career in 1999 as human resources manager for Starwood Hotels and Resorts Worldwide LLC, now a subsidiary of Marriott International Inc. She previously worked as director and manager in Starwood's housekeeping division.
Meier received a bachelor's degree in hotel/motel administration and management from Eastern Illinois University.
Bruce MacMillan, Chief Marketing Officer
Bruce MacMillan is responsible for PCMA's global brand development and marketing strategies as PCMA's Chief Marketing Officer. He leads the marketing, events and print and digital teams, which includes Convene magazine.
MacMillan has more than 30 years of experience in the global business events and tourism industry and has worked with business enterprises on every continent. His past leadership roles include CEO of VisitDFW, a regional consumer content marketing venture, CEO of Meeting Professionals International and CEO of Tourism Toronto.
He developed and led Vancouver, B.C.'s successful national bid for the 2010 Olympic Winter Games. MacMillan also runs BANDWIDTH consultancy, advising destinations on event sales and marketing strategies and served as consortium consulting partner in the Destinations International DestinationNEXT global initiative.
MacMillan has received numerous awards including twice being named one of the Top Twenty most influential people in the global MICE industry.
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text:
Q: In VBScript how do you take a string using mid and split the string at say a ";" So I am newer to VBScript and struggling taking a string and remove/splitting it. I currently have:
id= mid(storeline,id,instr(id,storeline, ";",1))

I essentially want to rid of any code after the ";".
For example: ID:12049302; Height = 20; I currently have it returning everything. Any help is awesome thanks.

A: You can use Split() to break your string down based on the ; delimiter value like so;
Dim storeline: storeline = "ID:12049302; Height = 20;"
Dim data: data = Split(storeline, ";")
Dim entry

If IsArray(data) Then
  'Return just the first entry
  WScript.Echo "Result is " & Trim(data(0) & "")

  'Use a loop to iterate through the Array
  For Each entry In data
    entry = Trim(entry & "")
    WScript.Echo entry
  Next
End If

Output:
Result is ID:12049302
ID:12049302
Height = 20

A: Assuming storeline = "ID:12049302; Height = 20;" then
myArray = Split(storeline, ";")
id = myArray(0) ' will contain "ID:12049302"

redpajama_set_name: RedPajamaStackExchange


Saturday passes were the first to go. Friday and Sunday tickets weren't far behind.
Lollapalooza single-day tickets for Aug. 1 sold out in less than 40 minutes after they went on sale this morning. Tickets for July 31 went moments later, and by noon all single-day passes had been snapped up.
Today's sale, charging $110 for each pass to attend one of the three days, began four hours after organizers announced who will be playing the massive Grant Park music festival, which runs July 31 through Aug. 2.
On Friday, Paul McCartney, Alt-J, the Weeknd and Alabama Shakes are set to headline. Cold War Kids, Sylvan Esso, Tove Lo and the War on Drugs are among the other acts scheduled.
Saturday headliners include Metallica, Sam Smith and Alesso. Kid Cudi, Walk the Moon, Django Django, Tame Impala and dozens of others are also scheduled to perform.
Sunday's lineup includes Florence and the Machine, Bassnectar and Of Monsters and Men, with acts such as A$AP Rocky, TV on the Radio, Odesza and Twenty One Pilots playing on the multiple stages around the festival site.
Three-day passes for the whole festival sold out in about 45 minutes yesterday, according to a Lollapalooza spokeswoman. Those eager festival-goers took a gamble buying tickets before the lineup was even announced. Both the $250 early bird and $275 regular three-day passes were all taken.
Last year, the early bird passes (priced at $225) sold out in about 15 minutes. In 2013, it took two hours for all the three-day passes to be scooped up.
Some Chase customers experienced difficulties yesterday when they tried to purchase their passes, but a Chase spokeswoman said the issue was resolved by the end of the day.
City officials estimate about 100,000 people jam Grant Park each day of the festival.


We all have a digital footprint, whether we like it or not. Back in 2013, I presented on How to build a successful personal brand at 300 Seconds. These days, no matter what sector you work in, having a professional social media presence is vital. When applying for jobs, many recruiters will check your digital footprint to see how you present yourself on LinkedIn, Twitter and even Facebook.
Having a strong personal brand not only helps you to climb the career ladder but it can also open up a host of new opportunities, such as presenting at conferences, invites to events or even writing opportunities.
Photographer Charlotte Knee, who has worked with Masterchef's Greg Wallace and Monica Galetti, Architect and TV presenter George Clarke and the Yammer team, interviewed me on the importance on personal branding and having a professional headshot.
I became an accredited trainer and have delivered training on behalf of Media Trust throughout the year.
Rob Dyson asked me to become an admin of The Third Sector PR and Communications Network – a hugely helpful network for advice, discussions or sharing resources. If you're not a member yet, what are you waiting for?
I was an official blogger for the Institute of Fundraising's National Convention – three days of great presentations and the opportunity to catch up with fellow charity folk.
I landed my current role doing a job I love for a company I've long admired.
My blog post on how to run a successful crowdfunding campaign was CharityComms most read article of 2014. Thanks to Anastasia Emmanuel from Indiegogo for her top tips!
Presenting with my colleague Deborah at Media Trust's Art of Engagement conference has definitely been a highlight, particularly as I don't like public speaking!
And talking about public speaking… I also presented recently at the IoF's Regional Special Interest Group for Community Fundraising and it was great as there was a lot of discussion and debate. I was followed by Teri Doubtfire who delivered a fantastic presentation – I've definitely taken some tips on presenting from her!
I've been a Trustee at the Small Charities Coalition for just over a year now and I'm really excited at the direction the charity is moving in.
Hopefully to pass Squared Online!
To help my team at work to reach our targets.
But generally… to work hard, to step out of my comfort zone, to say 'yes' more than 'no', to do the things that scare me and to just be happy.
What have been your highlights this year?
Have you got a life wish?
Life wishes. We've all got them right? My life wishes include: running a marathon, writing a book (would be great if it could top the Bestseller list but I can't be TOO fussy), visiting Machu Picchu, walking the Great Wall of China, renovating an old house into something Grand Designs would be proud of and learning to speak Italian.
'To live with my mom again. I miss her cuddles.
So I decided to stop procrastinating and do something to help Child's i raise the money they need to help trace and reunite babies and children that they provide short term emergency care for at Malaika. I want to inspire 100 people to sign up and raise £100 to do something on their 'life wish list'. That £100 is the difference between a child growing up in an orphanage or being reunited with their family.
So what will I be doing to raise £100? I'll be writing the first chapter of that book I've always wanted to write. Lucy Buck, Founder of Child's i, will be finding her inner voice by staying completely silent for 24 hours. Child's i's Kirsty Stephenson will be running 100 km in 100 days. What will you be doing?
If you can't take part then please help in other ways by spreading the word on social media, sponsoring a #100forChildsi team member or you can sponsor me. I'd be ever so grateful….
I am absolutely thrilled to announce that I have been appointed* as a Trustee for the Small Charities Coalition! The charity is a networking, mentoring and support organisation for small charities and is committed to helping staff, volunteers and trustees access the skills, knowledge and resources that they need to best serve their cause.
For those who know me, you will know that I embody the charity's mission wholeheartedly. With first-hand experience, I understand the challenges of working in a small charity and that is why I started the Sole Communicators group with CharityComms, over a year ago now, to give sole communicators a space to network with peers and share knowledge. It's also a professional development opportunity to develop their skills through our themed events with speakers from the sector. The next one takes place on 5 November with Helen Jones from Refuge who will be talking about their Don't Cover It Up campaign.
I also believe in giving back and sharing your skills with others on a one-to-one basis, which is why I have mentored small charities through Media Trust's Media Matching service and I'm currently a CharityComms mentor.
I really can't wait, in my capacity as a Trustee, to help the Small Charities Coalition spread the word about the vital work that they do to empower small charities and trustees with the skills they need to best serve their charities and, most importantly their supporters.
Alex Swallow, Chief Executive of the Small Charities Coalition, has written this brilliant blog post for Third Sector. I urge you to read it.
For a while now I've been sitting back admiring (and feeling a bit jealous at times) of my peers Matt Collins, Bertie Bosredon, Sam Phillips, Ben Matthews and Zoe Amar. I've been admiring the exciting projects they've been able to work on with a range of charities and clients and been a bit jealous of their ability to 'be their own boss'.
So I'm taking the plunge. I'm going freelance*.
I'm not going to lie….part of me finds the thought of the unpredictability of it all absolutely terrifying. But at the same time it's really, really, REALLY exciting (and oddly liberating) and I can't wait to get started.
Over the last month or so I have been meeting with accountants, setting up meetings with peers to get some advice, securing some work and getting a website in order (watch this space).
So I'm finishing my full time job next week and then I'm off on a little holiday before starting a part-time Social Media Consultancy role at a PR agency in the first week of September. I've also got a training course set up with another agency and I'm really excited about what we will be offering (more of that later).
While I get my website in order feel free to contact me via email, kirstymarrins(at)gmail(dot)com, or via Twitter or LinkedIn.
I look forward to hopefully working with you some day soon!
*Ok, so technically I'll be freelance three days a week.


text:
Interviewing 101, with KPCC's Kitty Felde
Does the thought of a microphone in your face turn your knees to jelly? Hate interviewing someone else to research your play or other project? How do you prepare? How do you handle handlers? How do you get close-mouthed people to open up? What is off the record? Never fear. "Interviewing 101" is on tap.
Whether you've interviewed dozens of people or working up to your first one, whether you interview people for print or electronic media, this experienced interviewer's experience will benefit you. Join KPCC's Special Correspondent and noted playwright Kitty Felde to learn the secrets of a successful interview.
Kitty Felde is a professional interviewer, having won numerous awards for her work. Before becoming Special Correspondent, Kitty Felde hosted KPCC's "Talk of the City" from 2001-2006, and did so part-time from 1997-2001.
In addition to her work in Los Angeles, she has reported from Africa and The Hague on AIDS and the war crimes tribunals for Rwanda and Bosnia. Most recently she produced the series on the Dodgers' move to Los Angeles and you'll periodically hear her "Street Stories," featuring the stories behind the names of L.A. roads.
When Kitty puts down her microphone, she puts on her pointe shoes in ballet class. She's also an award-winning playwright. Her work has been produced at the National Theater in Washington, D.C., and at various theaters in New York and Los Angeles. If you look very closely in Woody Allen's "Radio Days," you'll spot her playing the role of Mrs. Riley.

redpajama_set_name: RedPajamaCommonCrawl


Product Name: Recycled Paper Non-Woven Shopper Tote Item No: 3229213085324 Description: Made from 100% post-consumer material, this bag features a large open main compartment, 9" handle drop height, and cotton webbing handles and binding.
Imprint Area : L 8 in. x H 8 in.


text:
Q: Disable of caching in browser I'm using angular js views and routing to load different HTML inside a div.
But when i change an partial html and reload it stil shows up the cached version.
According to my reasearch this is not due to angular js template caching,
cause on load of html i tried to get the cached HTML like this $templateCache.get('loadedPage.html') and the result was undefined so its not angular js that is caching the html.
then when i saw in chrome i could find my html cached . i tried with following
<meta http-equiv="Cache-Control" content="no-cache, no-store, must-revalidate"/>
<META HTTP-EQUIV="Pragma" CONTENT="no-cache">

<meta http-equiv="Cache-Control" content="no-store" />
<meta http-equiv="cache-control" content="max-age=0" />
<meta http-equiv="cache-control" content="no-cache" />
<meta http-equiv="expires" content="0" />
<meta http-equiv="expires" content="Tue, 01 Jan 1980 1:00:00 GMT" />
<meta http-equiv="pragma" content="no-cache" />

but still i could see browser caching the html.
any other way of doing it ?

A: Its better to add some random query string or data to your js, so its prevent to cached in all browsers,
<script type="text/javascript">
document.write('<script src="script.js?'+Math.random()+'"></script>');
</script>


This affordable housing community consists of 25 unit townhomes in Cumberland, MD.
With 6 different footprints and a clubhouse, this 41,000 SF project included a total of 25 units varying in height from 2 to 3 stories. The exterior finishes of the buildings are a combination of brick veneer, EIFS, vinyl and cement board siding. Walls and floors are framed with wood, and roof construction consists of pre-engineered wood trusses.


text:
\section{Introduction}\label{sec-intro}
Bisimulation games \cite{CS1} have been defined for discrete procsses. Surpisingly,  there are no game semantics for similar relations with real time. In this paper, we extend bisimulation games to provide a coherent game structure for equivalence and preorder relations that involve real time. In \cite{VG1}, several semantic equivalences have been defined and compared in a model independent way. Some of these equivalences have been extended for real time as well. For example, there are well known notions of equivalences which include timed bisimulation and time abstracted bisimulation. In \cite{TY1}, equivalences even weaker than time abstracted bisimulation have been defined. They are time abstracted delay bisimulation and time abstracted observational bisimulation. In timed bisimulation, every time delay needs to be matched exactly which makes it a very strong form of equivalence. Time abstracted bisimulation on the other hand is a much weaker form of equivalence where a time delay by one process can be matched by any delay so that the respective derivatives are time abstracted bisimilar. To bridge this gap, in this paper we introduce \emph{interval bisimulation} which lies in between timed and time abstracted bisimulation. We can also conceive of a simulation relation corresponding to each of these bisimulation relations. In this work, we consider the hierarchy of these timed relations. Apart from proposing interval bisimulation and simulation equivalences corresponding to each well known bisimulation relation, the main contribution of this work includes proposing a generalized game semantics for these timed relations. This generalized game semantics will have certain parameters which being assigned different values can correspond to each of the relations shown in figure \ref{fig-timedSpectrum}. For the sake of completion of this spectrum of timed relations, we also include \emph{timed performance prebisimulation} which has been proposed in the recent work \cite{GNA1}. In this work, more particularly, we propose the game semantics for \emph{timed automata processes}. We choose timed automata since it is a well studied formalism and the decidability results for many of the relations based on timed automata are known. In contrast to Van Glabbeek's spectrum, at this point of time, we do not consider any form of trace equivalence in our work. We also do not consider either timed counterparts of relations like 2-nested simulation preorder or ready equivalence since the study of such relations are not known with respect to real time to the best of our knowledge. Game semantics for the equivalences in Van Glabbeek's spectrum  has been proposed in \cite{CD1}. In figure \ref{fig-timedSpectrum}, we present a spectrum of the timed relations mentioned above. In section \ref{sec-ta}, we present timed automata and its semantics briefly. In section \ref{sec-zone}, we present zone valuation graph as defined in \cite{GNA1}. Section \ref{sec-timedrels} describes several timed relations and compares them.   In section \ref{sec-timedgames}, we present the game characterizations of these timed relations. In section \ref{sec-gamehier}, we provide several lemmas that can be used to construct the hierarchy of the timed games. We conclude in section \ref{sec-conc}.
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{timedSpectrum.pdf}
\caption{\label{fig-timedSpectrum} Spectrum of timed relations}
\end{figure}

\section{Timed Automata}\label{sec-ta}
\emph{Timed automata}~\cite{AD1} is an approach to model time critical systems where the system is modeled with \emph{clocks} that track elapsed time. Timing of actions and time invariants on states can be specified using this model.

A timed automaton is a finite-state structure which can manipulate real-valued clock variables. Corresponding to every transition, a subset of the clocks can be specified that can be \emph{reset} to zero. In this paper, the clocks that are reset in a transition are shown as being enclosed in braces. Clock constraints also specify the condition for actions being enabled. If the constraints are not satisfied, the actions will be disabled. Constraints can also be used to specify the amount of time that may be spent in a location. The clock constraints $\mathcal{B}(C)$ over a set of clocks $C$ is given by the following grammar:
\begin{center}
$g ::= \; x \smile c \:|\: g \wedge g$
\end{center}
where $c \in \mathbb{N}$ and $x \in C$ and $\smile \: \in \: \{\le, <, =, >, \ge\}$.
A \emph{timed automaton} over a finite set of clocks $C$ and a finite set of actions $Act$ is a quadruple $(L,l_0, E, I)$ \cite{LAKJ1} where
$L$ is a finite set of locations, ranged over by $l$,
$l_0 \in L$ is the initial location,
$E \subseteq L \:\times\: \mathcal{B}(C) \:\times\: Act \:\times\: 2^C \:\times\: L$ is a finite set of \emph{edges}, and
$I\: : \: L \rightarrow \mathcal{B}(C)$ assigns invariants to locations.
\subsection{Semantics} The semantics of a timed automaton can be described with a \emph{timed labeled transition system}(TLTS)\cite{LAKJ1}. Let $A= \: (L, l_0, E, I)$ be a timed automaton over a set of clocks $C$ and a set of visible actions $Act$. The timed transition system $T(A)$ generated by $A$ can be defined as $T(A) = (Proc, Lab, \{\stackrel{\alpha}{\longrightarrow} | \alpha \in Lab\})$, where $Proc \: = \: \{(l,v)\:|\: (l,v) \in L \: \times \: (C \rightarrow \mathbb{R}_{\ge 0})$ and $v \models I(l)\}$, i.e. \emph{states}
are of the form $(l,v)$, where $l$ is a location of the timed automaton and $v$ is a valuation that satisfies the invariant of $l$. We use the terms \emph{process} and \emph{state} interchangeably in this text.
$Lab = Act \cup \mathbb{R}_{\ge 0}$ is the set of labels; and
the transition relation is defined by
$(l,v) \stackrel{a}{\longrightarrow} (l', v')$ if for an edge $(l \stackrel {g,a,r}{\longrightarrow}l') \in \: E$, $v \models g, v' = v[r]$ and $v' \models I(l')$, where an edge $(l \stackrel {g,a,r}{\longrightarrow}l')$ denotes that $l$ is the source location, $g$ is the guard, $a$ is the action, $r$ is the set of clocks to be reset and $l'$ is the target location. $(l,v)\stackrel{d}{\longrightarrow}(l, v+d)$ for all $d \in \mathbb{R}_{\ge 0}$ such that $v \models I(l)$ and $v+d \models I(l)$ where $v + d$ is the valuation in which every clock value is incremented by $d$.
Let $v_0$ denote the valuation such that $v_0(x)=0$ for all $x \in C$. If $v_0$ satisfies the invariant condition of the initial location $l_0$, then $(l_0, v_0)$ is the initial state or the initial configuration of $T(A)$.

\section{Graph Structure for Games}\label{sec-zone}
A bisimulation game \cite{CS1}\cite{CD1} is a two player game and consists of two \emph{graph structures} on which the game is played. The graphs are the visual representation of the two process descriptions for which the existence of a bisimulation relation has to be checked. For the games corresponding to timed equivalence and timed preorder relations too, we need to use a graph structure on which such timed games can be played. In this paper, we show how zone valuation graph \cite{GNA1} and some of its \emph{variants} are used as the graph structure on which the games corresponding to the timed relations are played. One must note that zone valuation graph \emph{cannot} be directly used in all the games discussed later. We may require certain modifications in the graph structure to characterize the games for various timed relations.

We briefly describe zone valuation graph. For this we first introduce zone and zone graph. The following two definitions are from \cite{WL1}.

\subsection{Zone Valuation Graph} \label{zonevalgraph}
\begin{definition} \textbf{zone:}
The characteristic set of a linear formula $\phi$, a clock constraint of the form $x \smile c$ or a diagonal constraint of the form $x - y \smile c$, where $x, y \in C$, is the set of all valuations for which $\phi$ holds. A zone is a finite union of characteristic sets.
\end{definition}

A \emph{zone graph} is similar to a \emph{region graph}\cite{LAKJ1} with the difference that each node consists of a timed automaton location and a zone.
\begin{definition}\textbf{zone graph:}
For a timed automaton $P = (L, l_0, E, I)$, a zone graph is a transition system $(S, s_0, Lep, \rightarrow)$, where $Lep = Act \cup \{\varepsilon\}$,
  $\varepsilon$ is an action corresponding to delay transitions of the processes of the zone, $S \subseteq L \times \Phi_{\vee}(C)$ is the set of nodes, $s_0 = (l_0, \phi_0(C))$, $\rightarrow \subseteq S \times Lep \times S$ is connected, $\phi_0(C)$ is the formula where all the clocks in $C$ are 0 and $\Phi_{\vee}(C)$ denotes the set of all zones.
\end{definition}
\begin{definition}\textbf{Bisimulation between zone graphs}
\item For two zone graphs, $Z_{1} = (S_1, s_1, Lep, \rightarrow_1)$ and $Z_{2} = (S_2,$ $s_2,$ $Lep,$ $\rightarrow_2)$, $Z_{1}$ is strongly bisimilar\cite{RM1} to $Z_{2}$, denoted as $Z_{1} \sim Z_{2}$, iff the nodes $s_1$ and $s_2$ are strongly bisimilar, denoted by $s_1 \sim s_2$.
\end{definition}
While checking strong bisimulation between the two zone graphs, $\varepsilon$ is considered visible similar to an action in $Act$. The $\varepsilon$ action represents a process delay $d \in \mathbb{R}_{\ge 0}$, where $d \ge 0$. Hence each node in the zone valuation graph has an $\varepsilon$ transition to itself. Besides as in region graph, $\varepsilon$ transitions are transitive in nature. To avoid clutter, the self loops and the transitive $\varepsilon$ transitions are not shown in any of the zone valuation graphs in this paper.
We present here zone valuation graph as defined in \cite{GNA1}. One should note that a zone valuation graph corresponds to a particular timed process or valuation of the timed automaton.

It is possible to have different zone graphs corresponding to a timed automaton. For a timed automaton $A = (L, l_0, E, I)$ and a process $r=(l_j,v_{l_j})\in T(A)$, we are interested in a particular form of zone graph Z$_{(A,r)}$=$(S, s_r, Lep, \rightarrow)$ which satisfies the following properties:
\begin{enumerate}
\item set $S$ is finite.
\item For every node $s \in S$ the zone corresponding to the constraints $\phi_s$ is convex.
\item $v_{l_j} \models \phi_{s_r}$. Note that $v_{l_j}$ may or may not satisfy $\phi_0(C)$.
\item \label{4} For any two processes $p,q\in T(A)$, if their valuations satisfy the formula $\phi_r$ for the same node $r \in S$ then $p \sim_u q$, i.e. $p$ is time abstracted bisimilar to $q$.
\item \label{5}For two timed automata $A_1$, $A_2$ and two processes $p \in T(A_1)$ and $q \in T(A_2)$, $Z_{(A_1,p)} \sim Z_{(A_2,q)} \Leftrightarrow p \sim_u q$.
\item It should be minimal to the extent of preserving convexity of the zones and gives a canonical form.
\end{enumerate}
For any node $s \in S$, let $\mathcal{G}(s)$ represent the set of all processes reachable from $p$ with the same location as that of $s$ and whose valuations satisfy $\phi_s$. $p$ is the initial clock valuation corresponding to which the zone valuation graph is created.
The following definitions are from \cite{GNA1}.
\begin{definition}{\textbf{Span:}}
 For a given node $s \in S$ and a clock $x \in C$, $min_{x}(s)$ and $max_{x}(s)$ represent the minimum and the maximum clock valuations of a clock $x$ across all processes in node $s$. For $x \ge c$, $min_x(s) = c$, for $x > c$, $min_x(s) = c + \delta$ and $max_x(s) = \infty$. For $x \le c$, $max_x(s) = c$, for $x < c$, $max_x(s) = c - \delta$ and $min_x = 0$ in both cases. Here $\delta$ is a symbolic representation of an infinitesimally small value. We define $range(x,s)$ as $max_{x}(s)-min_{x}(s)$. The span of a node $s \in S$ is defined as $\mathcal{M}(s) = min\{range(x,s)\ |\ x\in C\}$, i.e. minimum of all clocks' ranges. We define a clock $y$ belonging to the set $\{y \:|\: range(y, s) = \mathcal{M}(s)\}$ to be a critical clock of node $s$.
\end{definition}
 For example, in a zone valuation graph with two clocks $x$ and $y$, the span of a node $s$ with $\phi_s = x > 3$ and $y < 1$ is $min(\infty,1 - \delta)=1-\delta$ whereas span for a node with $\phi_s=x > 1$ and $y = 2$ is $min(\infty,0)=0$. We say that for a node $s$ in the zone valuation graph, $range(x, s) = m- l - 2\delta$ where valuations for clock $x$ lie in the range $l < x < m$. It is to be noted that $2\delta$ is also a symbolic value. It is to be noted that for a given node $s$, $range(x,s)$ is the same for all clock variables $x \in C$ if the zone corresponding to node $s$ is not abstracted with respect to any clock variable. If the zone corresponding to $s$ is abstracted with respect to one or more clock variables then for each such variable $x \in C$, $range(x,s)=\infty$. For example in figure \ref{fig-range}, we show a timed automaton and part of its zone valuation graph. The zone corresponding to rightmost node in the part of the zone valuation graph shown inthe figure, is abstracted with respect to clock $x$ and hence $range(x, s) = \infty$, whereas $range(y,s) = range(z, s) = 1 - 2 \delta$.
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{span_example.pdf}
\caption{\label{fig-range} Range of clocks in zone valuation graph node}
\end{figure}
\begin{definition}
Given a timed automaton $A$, let $Z_{(A, p)}$ be the zone valuation graph corresponding to process $p \in T(A)$. Let $p' \in T(A)$ be a process reachable from $p$ and $s$ be the node of $Z_{(A, p)}$ such that $p' \in \mathcal{G}(s)$. Let $x$ be a critical clock of $s$ and $v_{p'}(x)$ denote the valuation of clock $x$ for process $p'$. We define maximum admissible delay for $p'$ in $s$ as $max_{x}(s) - v_{p'}(x)$.
\end{definition}
For example, from the figure describing zone valuation graph for automaton 1 in figure \ref{fig-exTimeAbsDelayBisim} , the maximum admissible delay for the process $\langle A, x=1\rangle$ is $2-1= 1$.

The algorithm for creating zone valuation graph consists of two phases. In the first phase, forward and backward analysis of the given timed automaton produces a zone graph where zones are split based on a canonical decomposition \cite{TY1} of the constraints on the outgoing edges in the timed automaton. In the second phase, the nodes in the zone valuation graph produced after phase 1 that are strongly bisimilar to each other are merged using Paige-Tarjan algorithm \cite{PT1} to produce a canonical form of the zone valuation graph. After merging, every node in the zone valuation  graph denotes time abstracted bisimilar classes of the timed LTS of the given timed automaton that preserves convexity. Note that after phase 1, strongly bisimilar nodes corresponding to different locations of the timed automaton can also be combined. In such case, we say that the \emph{location set} of combined node is the set of locations of the nodes that are combined.

Forward analysis may cause a zone graph to become infinite \cite{BBFL1}. To ensure finiteness of the zone graph, several kinds of abstractions have been proposed in the literature \cite{DT1}\cite{BBFL1}\cite{BBLP1}. In \cite{GNA1}, \emph{location dependent maximal constants} abstraction \cite{BBFL1} is used to get a finite zone valuation graph.

The time complexity required for creation of zone valuation graph has also been derived given in \cite{GNA1}. In the worst case, the zone valuation graph created becomes same as region graph and hence the worst case complexity of creation of zone valuation graph is exponential in the number of clocks. For a given timed automaton, if $n$ be the number of locations in the timed automaton and $|S|$ and $m$ denote the number of nodes and edges respectively in the zone valuation graph produced after phase 1 of the algorithm, then the total time required in both phases for construction of the zone valuation graph is $O(n^2 (|C|^3n + |S| \times |C| +  n^2\times log\:n) + |S| \times log\:m)$.

\section{Equivalences and Preorders for Timed Systems}\label{sec-timedrels}
We discuss here several bisimulations, simulation equivalences and preorders dealing with real time for timed processes that are states or valuations of a timed automaton execution.
\begin{definition}\label{def-timedbisim}
\textbf{Timed bisimilarity}: A binary symmetric relation $\mathcal{R}_t$ over the set of states of a TLTS is a timed bisimulation relation if whenever $p_1 \mathcal{R}_t p_2$, for each action $a \in Act$ and time delay $d \in \mathbb{R}_{\ge 0}$\\[.1cm]
if $p_1 \stackrel{a}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{a}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_t p_2'$, and \\
if $p_1 \stackrel{d}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{d}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_t p_2'$.\\
Timed bisimilarity $\sim_t$ is the largest timed bisimulation relation.
\end{definition}
Timed automata $A_1$ and $A_2$ are \emph{timed bisimilar} if the initial states in the corresponding TLTS are timed bisimilar. Matching each time delay in one automaton with identical delays in another automaton may be too strict a requirement. Time abstracted bisimilarity is the relation obtained by a relaxation of this requirement where $p'_1 \sim_t p'_2$ is replaced uniformly by $p'_1 \sim_u p'_2$ and the second clause of definition \ref{def-timedbisim} is replaced by\\
\textit{if $p_1 \stackrel{d}{\rightarrow} p'_1$ then there is a transition  $p_2 \stackrel{d'}{\rightarrow} p'_2$, such that $p'_1 \sim_u p'_2$}.
The delay $d$ can be different from $d'$.\\[.1cm]
Timed automata $A_1$ and $A_2$ are \emph{time abstracted bisimilar} if the initial states in the corresponding TLTS are time abstracted bisimilar.

In this work, we introduce below \emph{interval bisimulation} to bridge the gap between timed and time abstracted bisimulation and provide its game semantics later indicating how it can be decided using zone valuation graph.
\begin{definition}\label{def-intvltimedbisim}
\textbf{Interval bisimilarity}: A binary symmetric relation $\mathcal{R}_i$ over the set of states of a TLTS is an interval bisimulation relation if whenever $p_1 \mathcal{R}_i p_2$, for each action $a \in Act$ and time delays $d, \:d' \in \mathbb{R}_{\ge 0}$\\[.1cm]
if $p_1 \stackrel{a}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{a}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_i p_2'$, and \\
if $p_1 \stackrel{d}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{d'}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_i p_2'$ and $d' = d$ if $frac(d) = 0$ and $d' \in (\:\lfloor d \rfloor, \lceil d \rceil\:)$ otherwise. Here frac(d) denotes the fractional part of delay $d$.\\
Interval bisimilarity $\sim_i$ is the largest interval bisimulation relation.
\end{definition}
\begin{definition}\label{def-delaybisim}
\textbf{Time Abstracted Delay Bisimilarity}: A binary symmetric relation $\mathcal{R}_y$ over the set of states of a TLTS is a time abstracted delay bisimulation relation if whenever $p_1 \mathcal{R}_y p_2$, for each action $a \in Act$ and time delays $d, \:d' \in \mathbb{R}_{\ge 0}$\\[.1cm]
if $p_1 \stackrel{a}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{d}{\rightarrow} \stackrel{a}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_y p_2'$, and \\
if $p_1 \stackrel{d}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{d'}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_y p_2'$.\\
Time abstracted delay bisimilarity $\sim_y$ is the largest time abstracted delay bisimulation relation.
\end{definition}
\begin{definition}
A time abstracted observational bisimulation relation, $\mathcal{R}_o$ can be defined by replacing $\mathcal{R}_y$ uniformly with $\mathcal{R}_o$ in definition \ref{def-delaybisim} and the first clause in definition \ref{def-delaybisim} being replaced by the following: \\
\emph{if $p_1 \stackrel{a}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{d_1}{\rightarrow} \stackrel{a}{\rightarrow} \stackrel{d_2}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_o p_2'$}.
Time abstracted observational bisimilarity, denoted by $\sim_o$, is the largest time abstracted observational bisimulation relation.
\end{definition}
\begin{definition}\label{def-timedsim}
\textbf{Timed Simulation}: A timed process $p_2$ is said to time simulate process $p_1$ if there exists a relation $\mathcal{R}_1$ such that for each action $a \in Act$ and time delay $d \in \mathbb{R}_{\ge 0}$\\[.1cm]
if $p_1 \stackrel{a}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{a}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_1 p_2'$, and \\
if $p_1 \stackrel{d}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{d}{\rightarrow} p_2'$ such that $p_1' \mathcal{R}_1 p_2'$.\\
$p_1$ and $p_2$ are said to be timed simulation equivalent if $p_1$ time simulates $p_2$ and $p_2$ time simulates $p_1$.
\end{definition}
Thus corresponding to each of the bisimulation relation defined above, we can define a simulation equivalence.

The following definition of timed performance prebisimulation is from \cite{GNA1}.
\begin{definition}\label{def-timedprebisim}
\textbf{Timed performance prebisimilarity}: A binary relation $\mathcal{B}$ over the set of states of a TLTS is a \emph{timed performance prebisimulation relation} if whenever $p_1 \mathcal{B} p_2$, for each action $a \in Act$ and time delay $d \in \mathbb{R}_{\ge 0}$\\[.1cm]
if $p_1 \stackrel{a}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{a}{\rightarrow} p_2'$ such that $p_1' \mathcal{B} p_2'$, and \\
if $p_2 \stackrel{a}{\rightarrow} p_2'$ then there is a transition $p_1 \stackrel{a}{\rightarrow} p_1'$ such that $p_1' \mathcal{B} p_2'$, and \\
if $p_1 \stackrel{d}{\rightarrow} p_1'$ then there is a transition $p_2 \stackrel{d'}{\rightarrow} p_2'$ for $d \le d'$ such that $p_1' \mathcal{B} p_2'$ ,and \\
if $p_2 \stackrel{d}{\rightarrow} p_2'$ then there is a transition $p_1 \stackrel{d'}{\rightarrow} p_1'$ for $d \ge d'$ such that $p_1' \mathcal{B} p_2'$.\\
Timed performance prebisimilarity $\precsim$ is the largest timed performance prebisimulation relation.
\end{definition}

\subsection{Comparison Among these Relations}
It is easy to see from the definitions that strong timed bisimulation implies strong time-abstracted bisimulation whereas the converse is not true. Interval bisimulation lies in between timed bisimulation and time abstracted bisimulation and from the definitions, $\sim_u \:\subseteq\: \sim_y \:\subseteq \:\sim_o$. Also existence of a bisimulation relation between two processes implies the existence of the corresponding simulation equivalence. It is also easy to see that timed performance prebisimulation lies in between timed bisimulation and time abstracted bisimulation. Though not immediately evident, we will subsequently prove that timed performance prebisimulation is weaker than interval bisimulation. In figure \ref{fig-timedSpectrum}, an arrow from one relation to the other denotes that the relation from which the arrow originates is stronger than the one to which it points. Hence we have $\sim_t \:\Rightarrow \:\sim_i \:\Rightarrow \:\precsim \:\Rightarrow \:\sim_u \:\Rightarrow \:\sim_y \:\Rightarrow \:\sim_o$ and it is easy to see that similar implication relations also exist among the corresponding simulation equivalences. Thus we obtain figure $\ref{fig-timedSpectrum}$ where $\mathcal{R}_1 \longrightarrow \mathcal{R}_2$ denotes that $\mathcal{R}_1$ is a strict subset of $\mathcal{R}_2$.

\section{Game Characterization}\label{sec-timedgames}
In \cite{CD1}, a hierarchy of games has been proposed that allows systematic comparison of process equivalences for discrete processes. The process hierarchy of Van Glabbeek can be embedded in the game hierarchy defined in \cite{CD1}. In this work we provide a similar game hierarchy so as to correspond to process equivalences and preorders that involve real time. Similar to the games in \cite{CD1}, our games are also Ehrenfeucht-Fra\"{\i}ss\'{e} games where player I is known as the \emph{attacker} and player II is called the \emph{defender}. The game is played on a finite graph. In our case this finite graph is either the zone valuation graph or one of its variants as described later in detail. Corresponding to the two timed processes for which we want to check if they are related through one of the relations described in section \ref{sec-timedrels}, two graphs are first created on which the game is to be played. As in every EF game, the attacker chooses a graph and makes its move. The defender tries to replicate the move on the other graph. If the defender can always replicate the move the attacker makes, then it wins implying that the two processes are related through the relation that corresponds to the game. If at any point in time, the defender cannot replicate the move of the attacker, then it loses which implies that the two processes are not related through the corresponding relation. In a bisimulation game before any round, the attacker can also choose the graph on which it will make its move. The defender has to choose the other graph. If the attacker changes the graph between two consecutive rounds, it is known as an \emph{alternation}. Alternations are not allowed in games corresponding to simulation equivalences. A game can be played infinitely or for a finite number of rounds. The moves made by the attacker or the defender can also differ from one game to another. In the EF games described in this section, the moves denote an action or a sequence of actions belonging to the set $Act \cup \{\varepsilon\}$. Certain extra conditions can also be part of the game depending on the relation to which the game corresponds to. For example, in timed bisimulation game, after every move the defender needs to ensure that the span of its current node is exactly same as the span of the node in which the attacker resides. Ensuring the equality of the span is an extra condition.

\subsection{Game Template}
A timed game proposed in this work can be described using the grammar $\mathcal{L} ::= n-\Gamma^{G, \alpha, \beta}_{k} \;, \; \mathcal{L}_1 \vee \mathcal{L}_2$. Each game is characterized by the following parameters as described below:
\begin{itemize}
\item $n$ : number of alternations. If not mentioned, it denotes no restriction on the number of alternations in the subgame.
\item $k$ : number of rounds; a subgame can have even infinite number of rounds.
\item $G$ : underlying graph on which the game is played. It can be of the following types: $Z$ denotes zone valuation graph, $Z_1$ denotes the graph obtained after phase 1 of zone valuation graph construction. This can be used for games of time abstracted relations. $Z_{sim}$ denotes the graph that is obtained by combining the nodes of $Z_1$ that are simulation equivalent.
\item $\alpha$ : a vector of two elements: the first element denotes the move chosen by attacker whereas the second element denotes the move chosen by defender.
\item $\beta$ : extra condition in the game and may be of the following types:
\begin{itemize}
\item $=$ : This condition denotes that span has to be matched. We also use $(s_1 = s_2)$ to denote that the spans of nodes $s_1$ and $s_2$ should be the same.
\item $\lfloor=\rfloor$ : This condition denotes that the integer portion of the span has to be matched and if the decimal part of one span is 0, then so should be for the other. We also sometimes use $(s_1 \lfloor = \rfloor s_2)$ where $s_1$ and $s_2$ are nodes of the two zone valuation graphs.
\item $G_1, \le$ : Let the two graphs for the two timed processes be denoted by $G_1$ and $G_2$. This extra condition denotes that the span of any node in $G_1$ should be less than or equal to the span of the corresponding bisimilar node in $G_2$.
\end{itemize}
$\beta$ if not specified denotes that there is no extra condition.
\end{itemize}

\subsection{Time Abstracted Bisimulation Game}
This is the EF bisimulation game played on the zone valuation graphs of two timed processes. There is no restriction on the number of rounds and the number of alternations.
\begin{lemma}
The game $\Gamma^{Z, \langle a, a \rangle}_{\infty}$, where $a \in Lep$ characterizes time abstracted bisimulation.
\end{lemma}
\proof This is a strong bisimulation game played on two zone valuation graphs. By construction of zone valuation graph, two processes are time abstracted bisimilar if their corresponding zone valuation graphs are strongly bisimilar. Hence the proof.
\qed
Note that for any kind of time abstracted relation, the zone graph obtained after phase 1 of the zone valuation graph creation algorithm can be used. The intuition behind this is that in phase 2, the zones that are behaviorally similar (bisimilar or simulation equivalent) are combined in this phase. Only the span of the combined zone changes which is required for matching the time. Thus phase 2 is important for timed relations only.
\begin{example}
Figure \ref{fig-exTimeAbsBisim} shows two timed automata and their corresponding zone valuation graphs for timed processes $\langle A, x = 0 \rangle$ and $\langle A',x =  0\rangle$. The defender has a universal winning strategy for the game $\Gamma^{Z, \langle a, a \rangle}_{\infty}$ and hence the two processes are time abstracted bisimilar.
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{untimedBisim_example.pdf}
\caption{\label{fig-exTimeAbsBisim} Example of time abstracted bisimulation game}
\end{figure}
\end{example}

\subsection{Timed Bisimulation Game}
This game is same as the game for time abstracted bisimulation but has an extra condition which specifies that the spans of every pair of bisimilar nodes from the two zone valuation graphs should be equal.
\begin{lemma}
The game $\Gamma^{Z, \langle a, a,\rangle, =}_{\infty}$, where $a \in Lep$ characterizes timed bisimulation.
\end{lemma}
\proof In this game if the defender has a universal winning strategy then it implies that the two zone valuation graphs are strongly bisimilar and every pair of bisimilar nodes in the two zone valuation graphs have equal span. This implies that the two timeed processes are timed bisimilar. The detailed proof is given in \cite{GNA2}.
\qed
\begin{example}
In this example, we consider two timed automata as given in \cite{LAKJ1}. Figure \ref{fig-exTimedBisim} shows the two timed automata and their corresponding zone valuation graphs for timed processes $\langle A, x = 0 \rangle$ and $\langle A', x = 0 \rangle$. The defender has a universal winning strategy for the game $\Gamma^{Z, \langle a, a \rangle, =}_{\infty}$ and hence the two processes are timed bisimilar. In  the figure, the spans of the nodes are indicated within parentheses.
\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{timedBisim_example.pdf}
\caption{\label{fig-exTimedBisim} Example of timed bisimulation game}
\end{figure}
\end{example}

\subsection{Interval Bisimulation Game}
This game is same as the game for timed bisimulation with the following difference. Let $s_p$ and $s_q$ be the initial nodes of the zone valuation graphs corresponding to processes $p$ and $q$. It is not required that the spans of $s_p$ and $s_q$ have to be equal but the integer parts of the spans should be the same and if the fractional part of one span is 0, so should be for the other node. Thus the game characterization for interval bisimulation is $\Gamma^{Z, \langle a, a \rangle, (s_p \lfloor = \rfloor s_q, s_1 = s_2)}_\infty$, where $(s_1, s_2) \neq (s_p, s_q)$ and $a \in Lep$.

\begin{theorem} \label{thm-interval}
A universal winning strategy for the defender in the game $\Gamma_{\infty}^{Z, \langle a, a\rangle, (s_p \lfloor = \rfloor s_q, s_1 = s_2)}$, where $(s_1, s_2) \neq (s_p, s_q)$ and $a \in Lep$ denotes that the two timed processes $p$ and $q$ are interval bisimilar. Here $s_p$ and $s_q$ are the initial nodes of the two zone valuation graphs.
\end{theorem}
\proof
For the initial nodes $s_p$ and $s_q$, $\lfloor \mathcal{M}(s_p)\rfloor  = \lfloor\mathcal{M}(s_q) \rfloor$, i.e. the integer portions of the spans match and $frac(\mathcal{M}(s_p)) = 0 \Leftrightarrow frac(\mathcal{M}(s_q)) = 0$ and for the rest of the bisimilar nodes from the two zone valuation graphs, their spans are equal $\Rightarrow \; \sim_i$. This implication is easy to see.\\[.2cm]
$\sim_i \; \Rightarrow$ for initial nodes $s_p$ and $s_q$, $frac(\mathcal{M}(s_p)) = 0 \Leftrightarrow frac(\mathcal{M}(s_q)) = 0$ and $\lfloor \mathcal{M}(s_p)\rfloor  = \lfloor\mathcal{M}(s_q) \rfloor$, i.e. the integer portions of the spans match and for the rest of the bisimilar nodes from the two zone valuation graphs, their spans have to be equal.

We prove this below. Considering the initial nodes, there can be two cases:
\begin{enumerate}
\item $frac(\mathcal{M}(s_{p}))$ = 0. By the definition of interval bisimulation $\mathcal{M}(s_{q}) = \mathcal{M}(s_{p})$.
\item when $frac(\mathcal{M}(s_{p})) \neq 0$. From the definition of interval bisimulation, this also requires that $frac(\mathcal{M}(s_{q})) \neq 0$.

Also it is straightforward to see that for $p$ and $q$ to be interval bisimilar, $\lfloor frac(\mathcal{M}
(s_{p})) \rfloor = \lfloor frac(\mathcal{M}(s_{q})) \rfloor$, i.e. their integer parts are the same. We
can prove this by contradiction. Suppose without loss of generality, the integer parts of the spans of $s_p$ and $s_q$ are respectively $t$ and $t + l$, where $t$ and $l$ are positive integers. Thus $p$ can make a delay $d = t+1$ to become $p'$ whereas $q$ cannot make a delay $t+1$ such that $q \stackrel{d=t+1}{\longrightarrow}{q'}$ and $p' \sim_i q'$ since such a $p' \not \in \mathcal{G}(s_p)$ whereas $q' \in \mathcal{G}(s_q)$.
\end{enumerate}
For the bisimilar nodes apart from the pair of initial nodes in the two zone valuation graphs, the spans have to be exactly same. The span of a node can be of the forms $t$, $t - \delta$ or $t - 2 \delta$, where $\delta$ symbolizes an infinitesimally small number.

Exactly with the same argument as above, we can show that two processes $p$ and $q$ cannot be interval bisimilar if any two bisimilar nodes in their corresponding zone graphs have spans $t$ and $t+l$, where $t$ and $l$ are positive integers.

Now we consider the case where the spans of two bisimilar nodes are $t$ and $t - \delta$. Let $p \stackrel{tr} {\longrightarrow} p'$, where $tr \in Lep^+$ and $p' \in \mathcal{G}(s_{p'})$ and $\mathcal{M}(s_{p'}) = t$. Similarly, let us suppose $q \stackrel{tr} {\longrightarrow} q'$ and $q' \in \mathcal{G}(s_{q'})$ and $\mathcal{M}(s_{q'}) = t - \delta$ and $s_{p'}$ and $s_{q'}$ form the pair of bisimilar nodes. We prove that in such a case $p$ and $q$ are not interval bisimilar.

Let in the paths from $s_p$ to $s_{p'}$ and from $s_q$ to $s_{q'}$, $s_{p_1}$ and $s_{q_1}$ be the first pair of nodes that are strongly bisimilar to each other such that the spans of $s_{p_1}$ and $s_{q_1}$ be $m$ and $m - \delta$ respectively. It is possible that $s_{p_1}$ is same as $s_{p'}$ and $s_{q_1}$ is same as $s_{q'}$. There can be two cases which can cause the span of $s_{q_1}$ to be $m - \delta$.
\begin{enumerate}
\item Lower limit of value of the critical clock $y$ is $j + \delta$ and the upper limit being $j + m$ where $j$ is an integer.
\item Lower limit of value of the critical clock $y$ is the integer $j$ and the upper limit being $j + m - \delta$.
\end{enumerate}
We start with the first case. Let $p_1 \in \mathcal{G}(s_{p_1})$ be the process such that $min_y(s_{p_1}) = v_{p_1}(y) = j$. Now we consider the transitions from $p$ to $p_1$ by delays of 1 time unit interspersed with visible action transitions. Process $q$ being interval bisimilar to $p$, performs the same actions. The delays of 1 time unit by the $p$-derivatives are exactly matched by the $q$-derivatives.

However, process $q$ by executing the same trace as executed by $p$ to evolve into $p_1$ will not lead into a process belonging to $\mathcal{G}(s_{q_1})$ since the valuation of every clock of the q derivative by executing the trace will be an integer and will not be of the form $j + \delta$. Thus $p$ and $q$ are not interval bisimilar if the lower limit of the valuation of their critical clocks are both not integers.

We can also prove similarly for the second case too that $p$ and $q$ will not be interval bisimilar.

Now let us consider the case where the spans of two bisimilar nodes are of the form $m$ and $m - 2 \delta$. Similar to the proof of the case where the spans are $m$ and $m - \delta$, it can be proved that processes $p$ and $q$ are not interval bisimilar. The proof for the case where the spans are of the form $m-\delta$ and $m  - 2\delta$ is also very similar.
\qed
\begin{corollary}
$p \sim_i q \Rightarrow p \precsim q$, where $p$ and $q$ are two timed processes.
\end{corollary}
\proof Suppose $p$ and $q$ are interval bisimilar and let their zone valuation graphs be $Z_{A_1, p}$ and $Z_{A_2, q}$ respectively with initial nodes $s_p$ and $s_q$. Without loss of generality, say $\mathcal{M}(s_p) \ge \mathcal{M}(s_q)$. Let $\mathcal{B}$ be a strong bisimulation relation such that for $(s_p, s_q) \in \mathcal{B}$, $\mathcal{M}(s_p) \ge \mathcal{M}(s_q)$ and for the rest of the pairs of bisimilar nodes in $\mathcal{B}$, their spans are equal. This implies that $\mathcal{B}$ is a timed performance prebisimulation relation.
\qed
\begin{example}
Figure \ref{fig-exTimeIntervalBisim} (a)  and (b) show two timed automata processes $\langle A, 2.4\rangle$ and $\langle A', 0.8\rangle$ and their corresponding zone valuation graphs in (c) and (d) respecively. The defender has a universal winning strategy for the game $\Gamma^{Z, \langle a, a \rangle, (s_p \lfloor = \rfloor s_q, s_1 = s_2)}_\infty$, where $(s_1, s_2) \neq (s_p, s_q)$ and $a \in Lep$ and hence the two processes are interval bisimilar Here $s_p$ and $s_q$ are the initial nodes of the zone valuation graphs corresponding to processes $\langle A, 2.4\rangle$ and $\langle A', 0.8\rangle$. Note that the two timed automata states $\langle A, 2.4\rangle$ and $\langle A', 0.8\rangle$
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{intervalBisim_example.pdf}
\caption{\label{fig-exTimeIntervalBisim} Figures (c) and (d) are zone valuation graphs for states $\langle A, 2.4\rangle$ and $\langle A', 0.8\rangle$ respectively}
\end{figure}
\end{example}

\subsection{Time Abstracted Delay Bisimualtion Game}
\begin{lemma}
The game $\Gamma^{Z, \langle a, \:\varepsilon \rightarrow a \rangle}_{\infty}$, where $a \in Lep$ characterizes time abstracted delay bisimualtion.
\end{lemma}
\proof: Since $\varepsilon$ in the graph represents a process delay, it is immediate from the definition of time abstracted delay bisimualtion.
\qed
\begin{example}
Figure \ref{fig-exTimeAbsDelayBisim} shows two timed automata and their corresponding zone valuation graphs for timed processes $\langle A, 0\rangle$ and $\langle A', 0\rangle$. $\langle A', 0\rangle$ can perform an $a$ action whereas $\langle A, 0\rangle$ can perform $a$ after performing an $\varepsilon$. The defender has a universal winning strategy for the game $\Gamma^{Z, \langle a, \:\varepsilon \rightarrow a \rangle}_{\infty}$ and hence the two processes are time abstracted delay bisimilar.
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{timeAbsDelayBisim.pdf}
\caption{\label{fig-exTimeAbsDelayBisim} Example of time abstracted delay bisimulation game}
\end{figure}
\end{example}

\subsection{Time Abstracted Observational Bisimulation Game}
\begin{lemma}
The game $\Gamma^{Z, \langle a, \:\varepsilon \rightarrow a \rightarrow \varepsilon \rangle}_{\infty}$ where $a \in Lep$ characterizes time abstracted observational bisimualtion.
\end{lemma}
\proof Immediate from the definition of time abstracted observational bisimulation game.
\qed
From the definition, this game can be defined as $\Gamma^{Z, \langle a, \:\varepsilon \rightarrow a \rightarrow \varepsilon \rangle}_{\infty}$ where $a \in Lep$.
\begin{example}
In figure \ref{fig-timeAbsObs}, two timed automata from \cite{TY1} are shown that are time abstracted observation bisimilar but not time abstracted delay bisimilar. Figure \ref{fig-timeAbsObsZone} shows the corresponding zone valuation graphs and we can see that the defender has a universal winning strategy for the game $\Gamma^{Z, \langle a, \:\varepsilon \rightarrow a \rightarrow \varepsilon \rangle}_{\infty}$.
\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{timeAbsObsBisim.pdf}
\caption{\label{fig-timeAbsObs} A and A' are time abstracted observation bisimilar but not time abstracted delay bisimilar}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{timeAbsObsZone.pdf}
\caption{\label{fig-timeAbsObsZone} Time abstracted observation bisimulation game for automata shown in figure \ref{fig-timeAbsObs}}
\end{figure}
\end{example}

\subsection{Time Abstracted Simulation Equivalence Game}
This game is similar to that of time abstracted bisimulation but dos not involve any alternation.
\begin{lemma}
The game is $0-\Gamma^{Z, \langle a, a \rangle}_{\infty}$ where $a \in Lep$ characterizes time abstracted simulation equivalence.
\end{lemma}
\proof Time abstracted simulation equivalence game can be considered to be a discrete simulation equivalence game which is a discrete bisimulation game without any alternation. Hence the proof.
\qed
Note that this game can also be played on the following zone graphs.
\begin{enumerate}
\item Like other time abstracted games, the zone graph $Z_1$ obtained after phase 1 of zone valuation graph generation.
\item A phase 2 can be executed, but in stead of combining the nodes that are strongly bisimilar to each other, the nodes that are simulation equivalent to each other are combined to get a canonical form of the zone valuation graph, where the nodes denote simulation equivalent classes of the timed automata valuations.
\end{enumerate}
On similar lines, we can also define the games for time abstracted delay bisimulation equivalence and time abstracted observational bisimulation equivalence as $0-\Gamma_{\infty}^{Z, \langle a,\: \varepsilon \rightarrow a\rangle}$ and $0-\Gamma_{\infty}^{Z, \langle a,\: \varepsilon \rightarrow a \rightarrow \varepsilon \rangle}$ respectively, where $a \in Lep$.

\subsection{Timed Simulation Equivalence Game}
Designing this game is tricky when the equivalence includes real time. In the untimed domain as in \cite{CD1}, a simulation equivalence game can be obtained from the bisimulation game by restricting the number of alternations to 0. In the timed version though, this is not the case. Thus the game $0-\Gamma^{Z, \langle a, a \rangle, =}_{\infty}$ where $a \in Lep$ does \emph{not} characterize timed simulation equivalence. This can be shown with the following example:
\begin{example}
Figure \ref{fig-exTimedSimEquiv} shows two timed automata and their corresponding zone valuation graphs for timed processes $\langle A, x= 0\rangle$ and $\langle A', x= 0\rangle$. In the first zone valuation graph, corresponding to location $A$, the nodes that are created are named $A_1$, $A_2$ and $A_3$ for convenience. The two processes are timed simulation equivalent though the defender does not have a universal winning strategy in the game $0-\Gamma^{Z, \langle a, a \rangle, =}_{\infty}$ as the spans of $A_1$ and $A'$ do not match. Note that here $A_1$ and $A_2$ are not strongly bisimilar and hence cannot be merged while creating the canonical form of the zone valuation graph through phase 2.
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{timedSimEquiv.pdf}
\caption{\label{fig-exTimedSimEquiv} $0-\Gamma^{Z, \langle a, a \rangle, =}_{\infty}$ game does not characterize timed simulation equivalence. It is characterized by $0-\Gamma^{Z_{sim}, \langle a, a \rangle, =}_{\infty}$.}
\end{figure}
\end{example}

Phase 2 is modified so as to merge the nodes that are simulation equivalent. Here $A_1$ and $A_2$ are simulation equivalent and thus can be merged to get $Z_{sim}$ on which the game can be played.The nodes of the graph $Z_{sim}$ denote the simulation equivalent classes of the corresponding timed LTS. The defender here has a universal winning strategy when the game is played on this variant of the zone valuation graph.
\begin{lemma}
The game $0-\Gamma_{\infty}^{Z_{sim}, \langle a, a \rangle, =}$ characterizes timed simulation equivalence.
\end{lemma}

\subsection{Timed Performance Prebisimulation Game}
In \cite{GNA1}, it has been shown that two timed processes are timed performance prebisimilar iff their zone valuation graphs are strongly bisimilar and for each pair of strongly bisimilar nodes, all nodes from one zone valuation graph should be equal to or smaller than the corresponding bisimilar node of the other graph. We can design the game as disjunction of two games. In the first game, while checking if the zone valuation graphs $G_1$ and $G_2$ are strongly bisimilar, we also check if the spans of the nodes of graph $G_1$ is less than or equal to the spans of corresponding bisimilar nodes of graph $G_2$. If the defender loses this game, then the second game is played which differs from the first subgame in the extra condition that now it is checked that if the span of the nodes in graph $G_2$ is less than or equal to the span of the bisimilar nodes of $G_1$. The game described above thus is $\Gamma_{\infty}^{Z, \langle a, a\rangle, (G_1, \le)} \: \vee \: \Gamma_{\infty}^{Z, \langle a, a\rangle, (G_2, \le)}$.
\begin{lemma}
The game $\Gamma_{\infty}^{Z, \langle a, a\rangle, (G_1, \le)} \: \vee \: \Gamma_{\infty}^{Z, \langle a, a\rangle, (G_2, \le)}$ characterizes timed performance prebisimulation.
\end{lemma}
\begin{example}
In this example, we consider the two timed automata from \cite{GNA1}. The two timed automata in figure \ref{fig-prebisimexample} are related through timed prebisimulation relation. The automaton in the left is \emph{at least as fast as} the automaton on the right, since the second $a$ action should be performed within a time interval of one time unit after the first $a$ action whereas in the second timed automaton, the second $a$ can be performed within an interval of two time units after the first action. The game $\Gamma_{\infty}^{Z, \langle a, a\rangle, (G_1, \le)} \: \vee \: \Gamma_{\infty}^{Z, \langle a, a\rangle, (G_2, \le)}$ is played on the their corresponding zone valuation graphs which are shown in figure \ref{fig-prebisimexamplecanozone}. The defender has a universal winning strategy.
\begin{figure}[t]
\centering
\includegraphics[width=0.6\textwidth]{prebisim_example.pdf}
\caption{\label{fig-prebisimexample} Example: Timed prebisimulation relation}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=0.7\textwidth]{prebisim_cano_zone.pdf}
\caption{\label{fig-prebisimexamplecanozone} Example: Zone valuation graph of timed automata shown in figures \ref{fig-prebisimexample}}
\end{figure}
\end{example}

\section{Hierarchy of Games} \label{sec-gamehier}
The following lemmas describe the hierarchy across different timed games that are obtained by assigning different values to each of the parameters in the game template. The arrow from the game on the left to the game on the right denotes that if the defender has a universal winning strategy for the game on the left, then it also has a universal winning strategy for the game on the right. Besides for each pair of games, if $\Gamma_1 \longrightarrow \Gamma_2$, then $\Gamma_2 \not \longrightarrow \Gamma_1$.
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{gamehierarchy.pdf}
\caption{\label{fig-gamehierarchy} Hierarchy of timed games}
\end{figure}
\begin{lemma}
$\Gamma_{\infty}^{G, \alpha, \beta} \longrightarrow n-\Gamma_{\infty}^{G, \alpha, \beta} $
\end{lemma}
This lemma states that if the defender has a universal winning strategy in a game with no restriction on alternations, then it will also win a game with finite number of alternations if the other parameters do not change.
\begin{lemma}
$\Gamma_{\infty}^{G, \alpha, \beta} \longrightarrow \Gamma_{k}^{G, \alpha, \beta} $
\end{lemma}
This lemma states that if the defender has a universal winning strategy in a game with infinite number of rounds, then it will also win in a game with finite number of rounds.
\begin{lemma}\label{lem-third}
$n-\Gamma_{k}^{G, \alpha, =} \longrightarrow n-\Gamma_{k}^{G, \alpha, \lfloor = \rfloor} $\\
$n-\Gamma_{k}^{G, \alpha, =} \longrightarrow n-\Gamma_{k}^{G, \alpha, (G_1, \le)} $\\
$n-\Gamma_{k}^{G, \alpha, =} \longrightarrow n-\Gamma_{k}^{G, \alpha, (G_2, \le)} $\\
$n-\Gamma_{1}^{G, \alpha, \lfloor = \rfloor} \longrightarrow n-\Gamma_{1}^{G, \alpha, (G_1, \le)} \: \vee \: n-\Gamma_{1}^{G, \alpha, (G_2, \le)}$\\
$n-\Gamma_{k}^{G, \alpha, \beta} \longrightarrow n-\Gamma_{k}^{G, \alpha} $
\end{lemma}
\begin{corollary}
$\Gamma^{Z, \langle a, a \rangle, (s_p \lfloor = \rfloor s_q, s_1 = s_2)}_\infty$ such that $(s_1, s_2) \neq (s_p, s_q)$ $\longrightarrow \Gamma_{\infty}^{Z, \langle a, a\rangle, (G_1, \le)} \:\vee \:\Gamma_{\infty}^{Z, \langle a, a\rangle, (G_2, \le)}$
\end{corollary}
This is immediate from lemma \ref{lem-third}.
\begin{lemma}
$n-\Gamma_{k}^{G, \langle a, a\rangle, \beta} \longrightarrow n-\Gamma_{k}^{G, \langle a, \varepsilon \rightarrow a \rangle, \beta} \longrightarrow n-\Gamma_{k}^{G, \langle a, \varepsilon \rightarrow a \rightarrow \varepsilon \rangle, \beta}$
\end{lemma}
This is true since every node in the zone valuation graph has an implicit edge labelled with $\varepsilon$. Here $a \in Lep$.
\begin{lemma}
$n-\Gamma_{k}^{Z, \langle a, a\rangle, \beta} \longrightarrow n-\Gamma_{k}^{Z_{sim}, \langle a, a\rangle, \beta}$
\end{lemma}
Thus assigning different values to each of these parameters $n_i$, $k_i$, $G_i$, $\alpha_i$, $\beta_i$ in the $i$th subgame, we can generate a complete game hierarchy using the lemmas given above. Below we give a diagram which shows the hierarchy of the games that correspond to the timed relations in figure \ref{fig-timedSpectrum}.
The diagram in figure \ref{fig-gamehierarchy} is only a small part of the entire hierarchy of timed games defined in this paper and as in \cite{CD1}, this leaves us with the scope of defining several timed relations or embed existing relations that are not discussed in this paper into this game hierarchy.

\section{Conclusion} \label{sec-conc}
In this paper, we have presented a hierarchy of games that can be played between two timed processes where these processes denote valuations of timed automata. Timed automata is a well studied formalism and the decidability results corresponding to several relations are known with respect to timed automata. The hierarchy among the games reflects the hierarchy among the timed relations. The game hierarchy also allows us to embed several other timed relations that are not discussed in this paper. The closest to our works are \cite{CS1} and \cite{CD1}. Bisimulation games were first introduced in \cite{CS1} and the game was extended in \cite{CD1} where similar EF games have been designed to characterize process equivalences appearing in Van Glabbeek's spectrum \cite{VG1}. As in \cite{CD1}, in our work too we provide a game template from which the entire hierarchy can be generated by assigning different values to the template parameters. However our case is more difficult since we deal with equivalences and preorders that involve real time. The main challenge here lies in designing the graph structure on which a game has to be played. We found that zone valuation graph introduced in \cite{GNA1} and its variants to be appropriate for this purpose.

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


As US plays role of skeptical parent, Iraqi Governing Council doesn't want to look like 25 James Deans.
It happens in every family: The kids want to strike out on their own, and the folks want to keep them under their wing a little bit longer.
Something like that breaking-away process is happening between the United States and Iraq's new leaders - some of them formerly exiled Iraqis the US nurtured and then installed in the interim Iraqi Governing Council.
The keepers of an ancient civilization may take offense at the parent-child analogy. But it nevertheless comes to mind as members of the US-appointed IGC - the learner's permit of what would be the world's newest democracy - make the rounds in New York at the United Nations and in Washington.
The group was sounding much more rebellious a few days ago, but by a press conference Wednesday at the UN, all talk of impatience or dispute with the power paying the bills was silenced - or at least on hold.
The speculation among skeptical journalists was that the Iraqis, led by Ahmed Chalabi, a former Pentagon protégé, got a talking-to.
Prefacing his remarks with an expression of gratitude to President Bush and the American people for "help[ing] us liberate ourselves from the scourge of Saddam Hussein," Mr. Chalabi said, "We have no disagreement with the US government."
That sounded different from earlier in the week, when Chalabi was saying - most notably in a front-page interview with The New York Times - that he wanted a faster transfer of sovereignty than what the US is proposing.
Another possibility was that once he got to New York, Chalabi - who holds the IGC's month-long rotating presidency - realized his show of independence wasn't going down well. For one thing, there is little enthusiasm aside from the French for a quick power transfer, and even the French appear to have modified their stance.
Chalabi appeared at the packed press conference with two IGC colleagues: Hoshyar Zebari, who holds the council's rotating foreign-minister slot, and Adnan Pachachi, a former UN envoy and Sunni Muslim representative on the council. Mr. Pachachi said he thought completing a constitution by May is realistic, while Mr. Zebari spoke in terms of an ideal full turnover of sovereignty within a year.
The three representatives displayed a united front, but even US officials say the 25-member council is not united on key issues. In Washington Wednesday, Iraq's White House-appointed administrator, Paul Bremer, acknowledged to the Senate Foreign Relations Committee that some IGC members want a quicker handover of responsibilities and political control.
But he said anything faster than what the US is advocating would be mistaken: "No appointed government, even one as honest and dedicated as the Iraqi Governing Council, can have the legitimacy necessary today to take on the difficult issues Iraqis face as they write a constitution and elect a government."
In any case, members of Congress and other Washington policymakers will have a chance to gauge the Iraqis' leadership skills next week, when the IGC members are set to visit the capital. Unless the Iraqis get cold feet, they are expected to claim they could do a better and cheaper job with some of the tasks the occupying authority now controls.
For example, the Iraqis say Mr. Bremer's and the rest of the American authority's dirty laundry is taken to neighboring Kuwait for washing, a job they say Iraqis could do at lower cost.
Demonstrations of independence from the Bush administration's vision could reemerge next week, some experts predict, when the Iraqis get around a divided Congress. But even at the UN, the distancing that takes place in the closest of families was showing.
The press conference venue was itself a symbol of that. The event was held in the small and stuffy meeting room of the UN Correspondents Association, even though a larger official briefing room, with adequate air conditioning and neat rows of baby-blue seating, sat empty upstairs. The Iraqis were not allowed access to that room since they are not an official UN delegation, not yet having officially replaced the Hussein regime.
Apparently, one briefly entertained option was to have the US sponsor the press conference and access the briefing room that way. But the US didn't relish the prospect of the international press blaring its sponsorship of the visiting Iraqis, some correspondents said. And, like adolescents who are testing their independence, the Iraqis didn't want to look like US protectorates anyway.


text:
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Sugarland's Jennifer Nettles Working on Solo Album With Rick Rubin, Sara Bareilles
By Billboard Staff | May 17, 2013 11:52 AM EDT
Sugarland's Jennifer Nettles Marries Longtime Boyfriend
Sugarland singer Jennifer Nettles announced today that she'll release her debut solo album this fall. The as-yet-untitled project is being produced by legendary producer Rick Rubin, who has flexed his rootsy side in the past with work on albums by Johnny Cash, Dixie Chicks and the Avett Brothers.
"I am absolutely thrilled and wholly proud to be working with Rick," Nettles said. "If you ask any musician who is on their producer 'bucket list,' Rick would be on each and every one."
Chatting with Rolling Stone, Nettles says,"I still get nervous around him, in a kind of a music-crush way."
Nettles, who gave birth to a son, Magnus, four months ago, says she's writing the songs herself or collaborating with artists like Sara Bareilles and Butch Walker. Rubin has assembled a backing band that includes Ian McLagan (Faces), Chad Smith (Red Hot Chili Peppers) and bassist Jason Lader.
Not involved with the album, at least currently, is Nettles' other half in Sugarland, Kristian Bush.
First things first, however, Nettles will be a presenter at the Billboard Music Awards on Sunday.
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The Dirty Nil Poke Fun at Social Media Posts About Self-Improvement on New Single
Hear the Hamilton band's track "Done with Drugs"
Hamilton rock trio the Dirty Nil are back with a new single, but don't let its title fool you. The song "Done with Drugs" is less a sobriety anthem and more a meta mockery of social media posts about sobriety.
The poppy, riff-heavy single will certainly get stuck in your head, but its lyrics about quitting drugs shouldn't be taken at face value.
Here's what frontman Luke Bentham had to say about it in a press release:
At this time in my life, I see a lot of people who are trying to stop doing cocaine or stop drinking rivers of liquor, or stop eating lots of shitty fast food. On Facebook, I see these posts from people declaring, "I'm done with this!" — they'll have a six-paragraph post about how they're changing their lives. I'm definitely not against self-betterment, and I'm not trying to make light of anyone's struggle; I'm just kind of amused and fascinated by that whole aspect of social media. Like someone will post, "I'm done drinking coffee!" Okay, well then just stop drinking coffee — you don't have to try to stop the internet for the day to tell everybody that you're done with Maxwell House! I find that funny, and somewhat narcissistic. But that's just my opinion, and I'm kind of an asshole!
Listen to "Done with Drugs" below.
The song can now be purchased on a 7-inch from Dine Alone, with a cover of Tom Petty's "Even the Losers" on the B-side.
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Lazies, Our new Maggie design is the perfect starting point for last minute holiday gifts like this cute 'Cafe Maggie' I received from Lazy Girl Lish. A few years back, Lish sent me a 'Wonder Cuppa', a Wonder Wallet filled with assorted drink options. Lish knows I'm a java gal! Well, below is Lish's latest incarnation of the Wonder Cuppa – it's the Cafe Maggie. Put some cocoa in there and it's Mocha Maggie!
Lish set the theme with this great coffee bean fabric. Then collected some drinkables and a condiment pack so I'd be ready to drink at a moment's notice. I like Lish more and more every day.
Everything fits in there with room to spare.
A nice assortment of coffee and tea is nice to take with me. Great to toss into any bag on my way out the door.
Consider putting your own collection and themed fabric and contents together to make a custom gift for a special loved one this season. Here are a few ideas to get you started.
First aid – antibiotic ointment, band aids, alcohol wipes.
Doggie details – plastic bags, treats, and for your hands – wet wipes.
Love – write special thoughts on small note cards to be read one per day.
Matched set – tuck a small Maggie inside a large Maggie for a matched set.
Remember, Maggie all by herself is wonderful gift, too. Give large Maggie for holding a camera or cell phone. Use small Maggie to give gift cards or cash.
Next Post » Show and Tell: More Maggie Frenzy!
Great ideas as always! I cut out several large Maggies last night and I think I'll tuck a packet of hot cocoa mix in each one. Also have planned a first aid Maggie for my teacher daughter. I already bought the bandaids and ibuprofen, just need to get the antibiotic wipes and I'm set.
Another idea is for dog walkers. Maggie would be perfect for holding plastic bags for cleaning up after your pup.
I'm glad Maggie is so fast and easy, because I have a lot to make!!
That is so funny!! I have three coffee fabrics cutout with the same idea in mind!!
I swear these are more addictive than the Wonder Wallets!
Love it and the coffee bean fabric sets the perfect tone!
Love it! Didn't think about a button hole (me the button freak!). So many ones on my machine. Great idea for the coffee mess (Navy term). I am teaching a class on Wednesday so I will let them know about another gift idea.
I picked up a set of winter themed stirrers to add to the pouch. I found my set at Kohl's but I've seem them other places. They stick out the edge of the Maggie and make a great addition to the hot cocoa.
i need to know where to purchase your patterns in the new england area.