text:
# Difference between revisions of "2020 AMC 10B Problems/Problem 16"

The following problem is from both the 2020 AMC 10B #16 and 2020 AMC 12B #14, so both problems redirect to this page.

## Problem

Bela and Jenn play the following game on the closed interval $[0, n]$ of the real number line, where $n$ is a fixed integer greater than $4$. They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in the interval $[0, n]$. Thereafter, the player whose turn it is chooses a real number that is more than one unit away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?

$\textbf{(A)} \text{ Bela will always win.} \qquad \textbf{(B)} \text{ Jenn will always win.} \qquad \textbf{(C)} \text{ Bela will win if and only if }n \text{ is odd.}$ $\textbf{(D)} \text{ Jenn will win if and only if }n \text{ is odd.} \qquad \textbf{(E)} \text { Jenn will win if and only if } n>8.$

## Solution

If Bela selects the middle number in the range $[0, n]$ and then mirror whatever number Jenn selects, then if Jenn can select a number within the range, so can Bela. Jenn will always be the first person to run out of a number to choose, so the answer is $\boxed{\textbf{(A)} \text{ Bela will always win}}$.

## Solution 2 (Guessing)

First of all, realize that the value of $n$ should have no effect on the strategy at all. This is because they can choose real numbers, not integers, so even if $n$ is odd, for example, they can still go halfway. Similarly, there is no reason the strategy would change when $n>8$.

So we are left with (A) and (B). From here it is best to try out random numbers and try to find the strategy that will let Bela win, but if you can't find it, realize that it is more likely the answer is $\boxed{\textbf{(A)} \text{ Bela will always win}}$ since Bela has the first move and thus has more control.

## Video Solution

https://youtu.be/3BvJeZU3T-M (for AMC 10) https://youtu.be/0xgTR3UEqbQ (for AMC 12)

~IceMatrix

 2020 AMC 10B (Problems • Answer Key • Resources) Preceded byProblem 15 Followed byProblem 17 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions
 2020 AMC 12B (Problems • Answer Key • Resources) Preceded byProblem 13 Followed byProblem 15 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 12 Problems and Solutions


text:
### Morality of Self Driving Cars

##### Mon Oct 22 2018

Although the movie I Robot has not aged well, it still brings up some interesting ethical questions that we are still discussing concerning self driving cars. The protagonist Detective Spooner has an almost unhealthy amount of distrust towards robots. In the movie, a robot decided to save Spooner’s life over a 12 year old girl in a car accident. This ignites the famous ethical debate of the trolley problem, but, now with artificial intelligence. The debate boils down to this: are machines capable of making moral decisions. The surface level answer from the movie is presented as no when Spooner’s presents car crash antidote. This question parallels the discussion that we are currently having with self driving cars. When a self driving car is presented with two options which result in the loss of life, what should it choose?

When surveyed, most people say that they would prefer to have self driving cars take the utilitarian approach towards the trolley problem. A utilitarian approach would try to minimize the total amount of harm. MIT made a neat website where it presents you with a bunch of “trolley problems” where you have to decide who dies. At the end of the survey the website presents you with a list of observed preferences you made when deciding who’s life was more important to save. The purpose of the trolley problem is merely to ponder what decision a self driving car should make when all of its alternatives are depleted.

### My College Essay

##### Fri Mar 16 2018

Students hate writing essays. It is easy to get wrapped up in the traditional 5 paragraph essay which is dull and boring. When writing a college essay, you have more freedom since you are telling a personal narrative. Since you are writing a story, you want to make it interesting. You should not rephrase the prompt which you are responding to, and you should not write about anything that the admissions office already knows. Your application already mentions all the clubs, classes, sports, and volunteer service you do– so don’t mention them.

I don’t want to go off on a huge tangent about how to write the perfect college essay, I’m not an expert. However, I would like to share my personal college essay which got me accepted into RIT and Clarkson last year. As a computer science applicant, it is a great idea to write your college essay based on the programming experience you had outside of school.

/**
* Title: HTTP ERROR 500
*
* Prompt: Describe a problem you’ve solved
*
* @author Jeffery Russell
*
* September 13, 2016
*/

#include <stdio.h>

main()
{
printf("

On a dim screen in the corner of my room flashed the dreadful message- HTTP
ERROR 500. That simple warning taunted, probed, and questioned my mind for
hours on end. As I pivoted my binocular gaze from the computer to out the
window, I saw the front yard dimly lit by the drowsy moon. Time for a second
stood still as the crickets chirped and the trees swayed in the cool summer
breeze. Closing my eyes for that second of silence made me realize how tired
I really was. A beeping, piercing, and dinging sound focused my gaze back to
the computer. Still flashing was that error reminding me that I had a long

For the past two weeks I had been working on an employee management system
for a store. This web based system was to keep track of employee hours for
payroll. The project was near complete; however, there was a few bugs left
to fix. The most annoying of which was password verification for the
webform. Now nearing the end of the development cycle, the project was
suppose to go live tomorrow.

Debugging a project is often a daunting task for programmers. Simply finding
an error is like finding a misspelled word in the dictionary. Correcting the
misspelling may be easy but finding that word is another story. What I love
about programming is that the program does exactly what I tell it to do. If
it makes a mistake it’s because I told it to, not because it feels tired, or
doesn't like me. Every bug, error, and glitch I unintentionally create.
These bugs eventually come out to the surface like a fish gasping for air.
An error is never just a mistake. It represents something much larger- an
error in my way of thinking. Debugging is a process that enables me to
further understand the program and crush the bug like the parasite it is.

Sitting back in my chair in deep thought I resumed the process of scanning,
poking, and probing my code for any source of the error. For the past hour I
narrowed the source of the error to ten lines of dubious code. Pondering
these lines of code I added an echo statement which allows me to see the
inner workings of the code. The error became as clear as day, the password
was not getting hashed: a feature that adds security to password storage.
Excitedly I typed a few lines of code to fix this problem. Then swiftly I
pressed execute, only to my disappointment to receive a different error
code. Eyes glazed over, I realized my mistake. In the process of debugging I
left a block of code commented out.

On a dim screen in the corner of my room beamed the message- Currently
Working.

");
}

# What are Deepfakes

We all know that you can do silly face swaps with snap chat and other apps. Previously face swapping faces on videos was terrible because you simply sequentially swapped all the faces frame by frame. As a result, the quality was very poor and did not handle head movements well. A Reddit user by the name of Deepfake created a recurrent neural net which accurately face swaps videos. Deepfake(the user) initially gathered a following by swapping celebrity faces onto porn videos.

Reddit has banned Deepfake and Pornhub has banned deepfakes from their platforms. Despite the attempts to remove fake deepfake videos, they are currently all over the internet.

# How Can You Make Deepfakes

### Why Do I Blog

##### Tue Feb 06 2018

It seems like there are millions of blogs on the internet. For every popular blog there is, there are hundreds of smaller blogs that go unnoticed. Should you start a blog if it will go unnoticed? Personally, I think the answer is yes. Different people may have different takes on this. There is an incentive to start a website in the hopes that it will become popular and make add revenue. However, I argue that there is a intrinsic value to a personal blog.

# Organize Your thoughts

Being able to clearly articulate your ideas is beneficial. Having time to brew over topics in a blog posts helps that process. Even though I worked with both Nodejs and PHP, I might not be able to a convincingly debate with somebody why one is the better platform. Writing a blog posts allows me to fully flesh out my own ideas.

# Learn

### Ways to Avoid Getting Hacked

##### Sat Dec 27 2014

Please note that these are just personal recommendations, and this article was written in 2014.

1. Avoid bad websites.

format: plain


text:
Name:

## PARIS, 18–21 SEPTEMBER 2013

Tutorial day: 18 SEPTEMBER

Conference: 19–21 SEPTEMBER

## The Problem

There is a distinct community in theoretical computer science, which studies logic, games and automata. Results produced by this community are dispersed across many conferences, which makes them difficult to follow, and the community rarely gathers. Also, since conferences are mainly used for publication, there are few incentives to make good talks, and some incentives to make bad ones (e.g. splitting one result into many conference papers).

## The Solution

A new conference: Highlights of Logic, Games and Automata. A visit to this conference gives you a wide picture of the latest research in the area. Also, a chance to meet everybody in the field, not just those who happen to publish in one particular proceedings volume. We intend to achieve this popularity by having no proceedings, a short and cheap event, and building on the tradition of the similar proceedings-free GAMES workshop.

## NO PROCEEDINGS

There are no proceedings. You present your best work, be it published elsewhere or yet unpublished.

## SHORT

The conference is two and a half days, preceded by one tutorial day. The contributed talks are around ten minutes or less.

## CHEAP

The conference fee will be at most 100€. Paris is easy to reach.

## EVERYBODY IS DOING IT!

Let's use the conference model that is so successful in other fields, like mathematics.

# Highlights 2013

## Paris, September 18–21

Tutorial day: September 18

Conference: September 19–21

## INVITED SPEAKERS

Patrice Godefroid

Erich Grädel

Marco Scarsini

Moshe Vardi

## TUTORIALS

Martin Grohe

Jérôme Leroux

Submission is closed.

We are unable to accept further registrations for the conference because the auditorium is at capacity. Likewise, there will be no possibility for registering on site. If you wish to attend the tutorials only, please write to the organisers.

### Wednesday 18 September — Tutorials

09:3013:00Tutorial
09:3013:00Jérôme Leroux Tutorial: The reachability problem for Petri nets
SLIDES speaker: Jérôme Leroux

#### Abstract

Systems equipped with counters are central when modeling distributed protocols, programs with recursive parallel threads, programs with pointers, broadcast protocols, databases, etc. When it comes to model-checking counter systems and their variants, the main results are that verification is undecidable when zero-tests are allowed, while several problems can be decided when zero-tests are forbidden — one speaks of VASS, for "vector addition systems with states", or equivalently "Petri nets". In the case of Petri nets, reachability was shown decidable in 1982, and the reachability problem for Petri nets and related decidable problems on subclasses of counter systems are pivot problems not only for the verification of infinite-state systems but also for problems appearing in very active research areas related to various logics and automata for data words/trees. Hence, the design of efficient algorithms for the reachability problem for VASS may have a great impact, not only in the realm of formal verification. It is however a very difficult problem. Therefore, improving the computational cost for solving the reachability problem for Petri nets would also improve the complexity of the formal verification of numerous classes of infinite-state systems.

Strikingly, the decision algorithm for Petri net reachability has never been implemented. This is because of its high complexity, both conceptual (the algorithm is very hard to understand and to describe) and computational (it is assumed that the complexity of the algorithm is not primitive-recursive). The general problem is known to be decidable by algorithms exclusively based on the classical Kosaraju-Lambert-Mayr-Sacerdote-Tenney decomposition (KLMTS decomposition). Recently, from this decomposition, it was proved that a final configuration is not reachable from an initial one if, and only if, there exists a Presburger inductive invariant that contains the initial configuration but not the final one. Since we can decide if a Presburger formula denotes an inductive invariant, we deduce from this result that there exist checkable certificates of non-reachability in the Presburger arithmetic. In particular, there exists a simple algorithm for deciding the general Petri net reachability problem based on two semi-algorithms. A first one that tries to prove reachability by enumerating finite sequences of actions and a second one that tries to prove non-reachability by enumerating Presburger formulas.

In this presentation, we provide a simple proof of the Petri net reachability problem that is not based on the KLMST decomposition. The proof is based on the notion of production relations, inspired from Hauschildt, that directly proves the existence of Presburger inductive invariants.

13:0014:30Lunch
14:3018:00Tutorial
14:3018:00Martin Grohe Tutorial: Logic for algorithms
SLIDES speaker: Martin Grohe

#### Abstract

The theme of this tutorial is (recent) applications of logic in the design and analysis of efficient algorithms. I will cover the following three topics.

1. Logical techniques in the analysis of generic algorithms

Certain generic (families of) algorithms, such as the Weisfeiler-Lehman algorithm for graph isomorphism testing and k-consistency tests for constraint satisfaction problems have logical characterisations. Thus logical techniques can be used to analyse the power of these algorithms and also to prove lower bounds for their running time.

2. Algorithmic meta theorems

Algorithmic meta theorems attempt to explain and unify algorithmic results by proving tractability not only for individual problems, but for whole classes of problems. These classes are typically defined in terms of logic. The prototypical example of an algorithmic meta theorem is Courcelle's Theorem, stating that all properties of graphs of bounded tree-width that are definable in monadic second-order logic are decidable in linear time.

In the tutorial, I will focus on meta theorems for first-order logic, where by now we have a fairly complete picture of graph classes admitting a nontrivial meta theorem

3. Applications of meta theorems in algorithmic graph structure theory

In this last part I will discuss applications of algorithmic meta theorems to problems in algorithmic graph structure theory. By this I mean graph algorithms that use meta theorems to solve tasks for which no other (direct combinatorial) algorithm is known.

It is worth noting that the algorithmic problems considered in all three parts are not derived from logic, such as satisfiability or model-checking problems, but "standard" algorithmic problems, often with a strong combinatorial and graph theoretical flavour. On the way, I will introduce the necessary graph theory, including nowhere dense graphs and certain aspects of graph minor theory.

### Thursday 19 September

09:0009:50Invited talk
09:0009:50Patrice Godefroid Invited talk: 500 Machine-years of software model checking and SMT solving
SLIDES speaker: Patrice Godefroid

#### Abstract

I will report on our experience running SAGE for over 500-machine years in Microsoft's security testing labs. SAGE is a whitebox fuzzing tool for security testing. It performs symbolic execution dynamically at the binary (x86) level, generates constraints on program inputs, and solves those constraints with an SMT solver in order to generate new inputs to exercize previously uncovered program paths or trigger security vulnerabilities (like buffer overflows). This process is repeated using novel state-space exploration techniques that attempt to sweep through all (in practice, many) feasible execution paths of the program while checking simultaneously many properties. This approach thus combines program analysis, testing, model checking and automated theorem proving (constraint solving). Since 2009, SAGE has been running 24/7 on average 100+ machines automatically fuzzing'' hundreds of applications. This is the largest computational usage ever for any SMT solver, with over 4 billion constraints processed to date. In the process, SAGE found many new security vulnerabilities (missed by blackbox fuzzing and static program analysis) and was credited to have found roughly one third of all the bugs discovered by file fuzzing during the development of Microsoft's Windows 7, saving millions of dollars by avoiding expensive security patches to nearly a billion PCs. In this talk, I will present the SAGE project, highlight connections with program verification, and discuss open research challenges. This is joint work with Michael Levin, David Molnar, Ella Bounimova, and other contributors.
09:5010:00Break
10:0011:12Session 1
10:0010:12Amélie Gheerbrant, Leonid Libkin and Cristina Sirangelo Incomplete information, monotonicity, and homomorphism preservation
SLIDES speaker: Cristina Sirangelo

#### Abstract

Incomplete information is ubiquitous in database applications, and yet our understanding of it is still rather basic. Since an incomplete database can represent multiple databases, query answering boils down to solving an entailment problem, while database systems are good at performing model-checking algorithms on first-order structures. Thus, to take advantage of them, we need to understand when entailment can be reduced to model-checking. We show that this happens for queries which are monotone with respect to the semantics of incompleteness, and that such monotonicity can be described via homomorphism preservation, for different notions of homomorphisms. Combining the latter with preservation theorems from logic (existing as well as new), we obtain classes of queries for which standard database systems can correctly compute answers over incomplete databases, or, logically speaking, for which entailment can be solved by simple model-checking.
10:1210:24Domagoj Vrgoč Querying graphs with data
SLIDES speaker: Domagoj Vrgoc

#### Abstract

With the recent resurgence of graph data model several languages for querying such data have been proposed. Traditionally these languages concentrated on querying topological properties while largely ignoring the actual data stored in the graph. In this presentation we will highlight how adding features that enable querying both data and topology affects the languages used to extract information from graph databases.
10:2410:36Pablo Barcelo, Gaëlle Fontaine, Miguel Romero and Moshe Y. Vardi Semantic acyclicity on graph databases
SLIDES speaker: Gaelle Fontaine

#### Abstract

Unions of acyclic conjunctive queries (CQs) can be evaluated in linear time, as opposed to arbitrary CQs, for which the evaluation problem is NP-complete. It is known that evaluation of semantically acyclic unions of CQs - i.e., unions of CQs that are equivalent to a union of acyclic ones - is tractable. We study the notion of semantic acyclicity in the context of graph databases and unions of conjunctive regular path queries (UCRPQs). We prove that checking whether a UCRPQ is semantically acyclic is decidable in 2ExpSpace and is ExpSpace-hard. We show that evaluation of semantically acyclic UCRPQs is fixed-parameter tractable.
10:3610:48Michael Vanden Boom Constructive interpolation for guarded logics
SLIDES speaker: Michael Vanden Boom

#### Abstract

The guarded fragment of first-order logic (GFO) shares many useful properties with modal logic, but fails to have Craig interpolation. Recently, an extension called the guarded negation fragment (GNFO) was shown to have interpolation, but the proof was non-constructive. The goal in this research (suggested by Benedikt, ten Cate, and Lutz) is to develop constructive methods for interpolation, in order to see whether interpolation can be performed in practice and to better understand the complexity of the problem. I describe some preliminary work on constructive interpolation for GNFO.
10:4811:00Eryk Kopczyński and Tony Tan Regular graphs and the spectra of two-variable logic with counting
SLIDES speaker: Eryk Kopczyński

#### Abstract

For a formula $\phi$ over a signature including predicates $P_1...P_k$, we define the image of $\phi$ as the set of tuples $(n_1...n_k)$ such that there is a model of $\phi$ where exactly $n_i$ elements satisfy $P_i$. For example, if each author has written exactly 2 papers, and each paper has exactly 3 authors, then 2*total number of authors=3*total number of authors. This can be seen as a generalization of the well known notion of a spectrum. Our main result is that, for formulae of FO2C, spectra and images are definable in Presburger arithmetic, and thus semilinear (and closed under complement).
11:0011:12Łukasz Kaiser and Charles Jordan Machine learning using descriptive complexity and SAT-solvers
SLIDES speaker: Lukasz Kaiser

#### Abstract

In machine learning there is an inherent trade-off between the efficiency of the learning algorithm and the expressiveness of the hypothesis that one is allowed to learn. Even though this trade-off is present in almost every machine learning task, it is hard to capture formally and still often resolved based on instinct and experience. We propose using parametrized logical formulas to represent hypotheses and then exploit propositional solvers for efficient learning and results from descriptive complexity to get expressiveness guarantees. This allows a more systematic study of the above trade-off and, as we show on a few examples, it is applicable to practical learning tasks.
11:1211:36Coffee break
11:3613:00Session 2
11:3611:48Florian Bruse, Oliver Friedmann and Martin Lange Polynomial guarded transformation for the modal mu-calculus is still open
SLIDES speaker: Florian Bruse

#### Abstract

Guarded normal form requires occurrences of fixpoint variables in a μ-calculus formula to occur under the scope of a modal operator. The literature contains guarded transformations that effectively bring a μ-calculus formula into guarded normal form. We show that the known guarded transformations can cause an exponential blowup in formula size, contrary to existing claims of polynomial behaviour. We also show that any poly- nomial guarded transformation for μ-calculus formulas in the more relaxed vectorial form gives rise to a polynomial solution algorithm for parity games, the existence of which is an open problem.
11:4812:00Paul Hunter The expressive completeness of Metric Temporal Logic
SLIDES speaker: Paul Hunter

#### Abstract

LTL has emerged as the primary logic for specifying temporal properties. This is largely due to the low complexity of its associated model checking problem and its high expressibility - with the celebrated result of Kamp showing that LTL has the same expressive power as first-order logic. In the quantitative setting, Metric Temporal Logic is quickly becoming the standard to which all other temporal logics are compared. It turns out that the expressive power of MTL is dependent on the set of constants available, and I will give a precise characterization of when MTL has the same expressive power as first-order logic.
12:0012:12Frederik Harwath and Nicole Schweikardt On the locality of arb-invariant first-order logic with modulo counting quantifiers
SLIDES speaker: Frederik Harwath

#### Abstract

We study Gaifman and Hanf locality of an extension of first-order logic with modulo p counting quantifiers (FO+MODp, for short) with arbitrary numerical predicates. We require that the validity of formulas is independent of the particular interpretation of the numerical predicates and refer to such formulas as arb-invariant formulas. We give a detailed picture of locality and non-locality properties of arb- invariant FO+MODp.
12:1212:24Wojciech Czerwiński, Wim Martens and Tomas Masopust Efficient separability of regular languages by subsequences and suffixes
SLIDES speaker: Wojciech Czerwiński

#### Abstract

When can two regular word languages K and L be separated by a simple language? We investigate this question and consider separation by piecewise- and suffix-testable languages and variants thereof. We give characterizations of when two languages can be separated and present an overview of when these problems can be decided in polynomial time if K and L are given by nondeterministic automata.
12:2412:36Thomas Place, Lorijn van Rooijen and Marc Zeitoun Separating regular languages by piecewise testable and unambiguous languages
SLIDES speaker: Lorijn van Rooijen

#### Abstract

We discuss the separation problem for regular languages. We give a Ptime algorithm to check whether two given regular languages are separable by a piecewise testable language, that is, whether a $\mathcal{B}\Sigma_1(<)$ sentence can witness that the languages are disjoint. If this is possible, we express a separator by saturating one of the original languages by a suitable congruence. Following the same line, we show that one can also decide whether two regular languages can be separated by an unambiguous (i.e. $FO^2(<)$-definable) language, albeit with a higher complexity.
12:3612:48Richard Mayr and Lorenzo Clemente Advanced automata minimization
SLIDES speaker: Richard Mayr

#### Abstract

12:4813:00Nathanaël Fijalkow, Krishnendu Chatterjee, Thomas Colcombet, Florian Horn, Denis Kuperberg,Michał Skrzypczak and Martin Zimmermann Boundedness games
SLIDES speaker: Nathanael Fijalkow

#### Abstract

In this talk, I will discuss some recent developments about boundedness games. They are two-player games played over graphs, featuring counters. The first player's objective is to satisfy a parity condition and that the counter values are bounded. A lot of questions are open: what is the algorithmic complexity of deciding the winner, and does there always exist finite-memory winning strategies? In particular, as shown by Thomas Colcombet, proving the existence of finite-memory winning strategies for (some) boundedness games is the last missing item to prove the decidability of cost-MSO over infinite trees. I will give an overview of where we stand now and what are the next challenges.
13:0014:30Lunch
14:3615:24Session 3
14:3614:48Olivier Carton and Luc Dartois Aperiodic two-way transducers
SLIDES speaker: Dartois Luc

#### Abstract

A two-way transducer is a finite state sequential machine with a two-way input tape and a one-way output tape. At each step of the computation, it reads the current symbol, outputs a possibly empty word, then changes its internal state and moves its input head, according to the transition taken with current state and the letter read. It computes a partial function from words over an alphabet to another set of words. Similarly, a MSO-definable function over words is defined as interpretations of linear graphs through logic. A result by Engelfriet and Hoogeboom proved the equivalence of the two models. I will recall the definition of both models, and state an extension of this result to the natural subclass of aperiodic two-way transducers.
14:4815:00Laure Daviaud and Thomas Colcombet Approximate comparison of distance automata
SLIDES speaker: Laure Daviaud

#### Abstract

Distance automata are automata weighted over the semiring (N U {+infinity},min,+) that compute functions from words to N U {+infinity}. It is known that testing f0 and two functions f,g computed by distance automata, answers "yes" if f(1+e)g(w), and may answer "yes" or "no" in all other cases. This is a joint work with Thomas Colcombet.
15:0015:12Rajeev Alur and Mukund Raghothaman Decision problems for additive regular functions
SLIDES speaker: Mukund Raghothaman

#### Abstract

We introduce cost register automata (CRA) -- this is a deterministic model to associate costs with strings that is parametrized by operations of interest (such as addition, scaling, and minimum), and a notion of regularity that provides a yardstick to measure expressiveness. Our notion of regularity relies on the notion of string-to-tree transducers, and allows associating costs with events that are conditioned on regular properties of future events. CRAs compute regular functions using multiple write-only registers whose values can be combined using the allowed set of operations. We then discuss various analysis problems associated with CRAs and regular functions, including the decidability of equivalance and containment, register and state minimization, and Angluin-style learning of cost functions.
15:1215:24Sylvain Lombardy and Jacques Sakarovitch The validity of weighted automata
SLIDES speaker: Jacques Sakarovitch

#### Abstract

This work addresses, and proposes a solution to, the problem of the validity of weighted automata in which epsilon-transitions may result in infinite summations. With a topological approach, a definition of validity is taken that insures that any closure algorithm will succeed on every valid weighted automaton. This definition is stable with respect to natural transformations of automata. Validity is shown to be decidable when weights are taken in Q or R. The corresponding algorithm is implemented in the VAUCANSON platform. The problem remains open in general.
15:2415:36Break
15:3616:48Session 4
15:3615:48Stanislav Böhm, Stefan Göller and Petr Jančar Equivalence of deterministic one-counter automata is NL-complete
SLIDES speaker: Stefan Göller

#### Abstract

We prove that language equivalence of deterministic one- counter automata is NL-complete. This improves the super- polynomial time complexity upper bound shown by Valiant and Paterson in 1975. Our main contribution is to prove that two deterministic one-counter automata are inequivalent if and only if they can be distinguished by a word of length polynomial in the size of the two input automata.
15:4816:00Stéphane Demri, Diego Figueira and M. Praveen Reasoning about data repetitions with counter systems
SLIDES speaker: Diego Figueira

#### Abstract

We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or past. We demonstrate correspondences between satisfiability problems for logics and reachability-like decision problems for counter systems. We show that allowing/disallowing atomic formulas expressing repetitions of values in the past corresponds to the reachability/coverability problem in Petri nets. This gives us 2EXPSPACE upper bounds for several satisfiability problems. We prove matching lower bounds by reduction from a reachability problem for a newly introduced class of counter systems. This new class is a succinct version of vector addition systems with states in which counters are accessed via pointers, a poten- tially useful feature in other contexts. We strengthen further the correspondences between data logics and counter systems by characterizing the complexity of fragments, extensions and variants of the logic. For instance, we precisely characterize the relationship between the number of attributes allowed in the logic and the number of counters needed in the counter system.
16:0016:12Michael Benedikt, Stefan Göller, Stefan Kiefer and Andrzej Murawski Bisimilarity of pushdown automata is nonelementary
SLIDES speaker: Stefan Göller

#### Abstract

Given two pushdown systems, the bisimilarity problem asks whether they are bisimilar. While this problem is known to be decidable our main result states that it is nonelementary, improving EXPTIME-hardness, which was the previously best known lower bound for this problem. Our lower bound result holds for normed pushdown systems as well.
16:1216:24Ranko Lazic, Joel Ouaknine and James Worrell Zeno, Hercules and the Hydra: Downward rational termination is Ackermannian
SLIDES speaker: Ranko Lazic

#### Abstract

Metric temporal logic (MTL) is one of the most prominent specification formalisms for real-time systems. Over infinite timed words, full MTL is undecidable, but satisfiability for its safety fragment was proved decidable several years ago. The problem is also known to be equivalent to a fair termination problem for a class of channel machines with insertion errors. However, the complexity has remained elusive, except for a non-elementary lower bound. Via another equivalent problem, namely termination for a class of rational relations, we show that satisfiability for safety MTL is not primitive recursive, yet is Ackermannian, i.e., among the simplest non-primitive recursive problems. This is surprising since decidability was originally established using Higman's Lemma, suggesting a much higher non-multiply recursive complexity.
16:2416:36Aleksy Schubert, Daria Walukiewicz-Chrząszcz and Paweł Urzyczyn Positive logic is not elementary
SLIDES speaker: Daria Walukiewicz-Chrząszcz

#### Abstract

We prove that the positive fragment of minimal first-order intuitionistic logic is not of elementary complexity. The proof uses an automata-theoretic approach taking advantage of the computational power of alternation.
16:3616:48Sylvain Schmitz Complexity hierarchies beyond elementary
SLIDES speaker: Sylvain Schmitz

#### Abstract

Decision problems with a non-elementary complexity occur naturally in logic, combinatorics, formal language, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond. Somewhat surprisingly, we lack the definitions of classes and reductions that would allow to state completeness results at such high complexities. We introduce a hierarchy of fast-growing complexity classes and discuss its suitability for completeness statements of non-elementary problems.
16:4817:12Coffee Break
17:1218:24Session 5
17:1217:24Thomas Brihaye and Quentin Menet Simple strategies for Banach-Mazur games and fairly correct systems
SLIDES speaker: Thomas Brihaye

#### Abstract

In 2006, Varacca and Voelzer proved that on finite graphs, omega-regular large sets coincide with omega-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try to understand relations between sets of probability~1 and various notions of simple strategy (including those introduced in a recent paper of Graedel and Lessenich). Then, we introduce a generalisation of the classical Banach-Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability~1 (as classical Banach-Mazur games characterise large sets). We obtain a determinacy result for these games, when the winning set is a countable intersection of open sets.
17:2417:36Thomas Brihaye, Gilles Geeraerts, S. Krishna, Lakshmi Manasa and Ashutosh Trivedi On the decidability of priced timed games
SLIDES speaker: Thomas Brihaye

#### Abstract

Two-player zero-sum games on finite automata are a classical metaphor for controller synthesis. An extension of this model to time-critical systems are two-player games on priced timed automata. For those games, the optimal reachability synthesis problem asks to compute a strategy (for one of the players) that guarantees to reach a given target with a total cost satisfying some optimality constraint. While, some versions of this problem have already been showed undecidable, we propose to complete the global picture by studying other variants (such as the timed-bounded version).
17:3617:48Krishnendu Chatterjee Survey of recent results for stochastic games
SLIDES speaker: Krishnendu Chatterjee

#### Abstract

Stochastic games provide a powerful framework to model fundamental problems in the design and analysis of stochastic reactive systems. While this connection is well understood, and several results have enriched the framework, there is a wealth of research questions that are open, including some long-standing ones (such as the complexity of perfect-information stochastic reachability games). In this talk, I will survey some recent results for general model of stochastic games and related models. The talk is based on several papers, and presents an overview of recent results based on joint works with several co-authors, as well as results from other researchers.
17:4818:00Mahsa Shirmohammadi, Laurent Doyen and Thierry Massart Synchronization in Markov decision processes

#### Abstract

Markov Decision Processes (MDPs) are 1-1/2 player stochastic games. The player tries to maximize the probability to satisfy an objective. Traditionally, the objective of the player is expressed as a set of desired sequences of states visited during the game. Recently, MDPs are viewed as generators of probability distributions over states, and objectives are defined as sets of sequences of probability distributions. We study synchronizing objectives that require that some state tend to accumulate all the probability mass. We consider three winning modes: sure, almost-sure and limit-sure.
18:0018:12Tomáš Brázdil, Holger Hermanns, Jan Krčál, Jan Kretinsky and Vojtĕch Řehák Verification of open interactive Markov chains
SLIDES speaker: Jan Kretinsky

#### Abstract

We provide the first assume-guarantee reasoning for stochastic continuous-time systems. Interactive Markov chains (IMC) are compositional behavioural models similar to continuous-time Markov decision processes. Given a time-bounded property and an IMC component, we synthesize its scheduler optimizing the probability that the property is satisfied when the IMC is working in an unknown environment. We also give a specification formalism for IMC and consider unknown environments satisfying a given specification.
18:1218:24Tomáš Brázdil, Antonin Kučera, Vojtĕch Forejt and Krishnendu Chatterjee Trading performance for stability in Markov decision processes
SLIDES speaker: Tomas Brazdil

#### Abstract

We study the central controller synthesis problems for finite-state Markov decision processes, where the objective is to optimize both the expected mean-payoff performance of the system and its stability. We argue that the basic theoretical notion of expressing the stability in terms of the variance of the mean-payoff (called global variance in our paper) is not always sufficient, since it ignores possible instabilities on respective runs. For this reason we propose alernative definitions of stability, which we call local and hybrid variance, and which express how rewards on each run deviate from the run's own mean-payoff and from the expected mean-payoff, respectively. We show that a strategy ensuring both the expected mean-payoff and the variance below given bounds requires randomization and memory, under all the above semantics of variance. We then look at complexity of the problem of determining whether there is a such a strategy.

### Friday 20 September

09:0009:50Invited Talk
09:0009:50Erich Grädel Invited talk: Linear Algebra and the quest for a logic for PTIME
SLIDES speaker: Erich Grädel

#### Abstract

The quest for a logic for PTIME is one of the central open problems in both finite model theory and database theory. It asks whether there is a logic in which a property of finite structures is definable if, and only if, it is decidable in polynomial time. Much of the research in this area has focused on the logic FPC, the extension of least or inflationary fixed-point logic by counting terms. In fact, FPC has been shown to capture PTIME on many natural classes of structures. On the other side, already in 1992, a graph query has been constructed that can be decided in PTIME but is not definable in FPC. But while this CFI query, as it is now called, is very elegant and has led to new insights in many different areas, it can hardly be called a natural problem in polynomial time. Therefore it was often remarked that possibly all natural polynomial-time properties of finite structures could be expressed in FPC. However, this hope was eventually refuted in a strong sense by Atserias, Bulatov and Dawar who proved that the important problem of solvability of linear equation systems (over any finite Abelian group) is not definable in FPC and that, indeed, the CFI query reduces to this problem. This motivates the study of the relationship between finite model theory and linear algebra, and suggests that operators from linear algebra, such as matrix ranks or solvability operators, could be a source of new extensions to fixed-point logic, in an attempt to find a logical characterisation of PTIME. We will discuss such approaches and study the relations between different polynomial-time computable problems over (finite) rings, fields and Abelian groups in the context of logical many-to-one and Turing reductions, i.e., interpretations and generalised quantiers. In this context, we will also discuss an alternative approach towards a logic for PTIME, proposed by Blass, Gurevich and Shelah, based on choiceless computations operating directly on structures.
09:5010:00Break
10:0011:12Session 6
10:0010:12Matthew Anderson and Anuj Dawar On symmetric circuits and FPC
SLIDES speaker: Anuj Dawar

#### Abstract

We study queries on graphs (and other relational structures) defined by families of Boolean circuits that are invariant under permutations of the vertices. In particular, we study circuits that are symmetric, that is, circuits whose invariance is explicitly witnessed by automorphisms of the circuit induced by the permutation of their inputs. We show a close connection between queries defined on structures by uniform families of symmetric circuits and definability in fixed-point logics.
10:1211:24Steven Lindell and Scott Weinstein Presentation-invariant definability
SLIDES speaker: Steven Lindell

#### Abstract

We extend the notion of invariant elementary definability to a variety of different graph representations, including those that strictly extend the power of first-order logic with an arbitrary linear order.
11:2410:36Robert Ganian, Petr Hliněný, Daniel Kral, Jan Obdržálek, Jarett Schwartz and Jakub Teska FO model checking of interval graphs
SLIDES speaker: Jan Obdržálek

#### Abstract

We study the computational complexity of the model checking problem for the first order (FO) logic on interval graphs, i.e., interscetion graphs of intervals on the real line. As the main result we show that for n-vertex interval graphs this problem can be solved in time O(n log n) if we take intervals with lengths from a fixed finite set. On the other hand, we show that this is no longer true once the interval lengths taken from any set that is dense in some open subset.
10:3611:48Oleg Verbitsky Bounds for the quantifier depth in two-variable logics
SLIDES speaker: Oleg Verbitsky

#### Abstract

Given structures $G$ and $H$ and a first-order formula $F$ over the same vocabulary, we say that $F$ distinguishes $G$ from $H$ if $F$ is true on $G$ but false on $H$. By alternation depth of $F$ we mean the maximum length of a sequence of nested alternating quantifiers in $F$. Obviously, this parameter is bounded from above by the quantifier depth of $F$. We will examine the maximum alternation depth and quantifier depth needed to distinguish two structures in two-variable first-order logic and its fragments. Lower bounds for the quantifier depth in the existential-positive fragment have applications to analysis of the computational complexity of Arc Consistency testing, one of the most popular heuristics for the constraint satisfaction problem.
10:4811:00Lucas Heimberg, Dietrich Kuske and Nicole Schweikardt An optimal Gaifman normal form construction for structures of bounded degree
SLIDES speaker: Lucas Heimberg

#### Abstract

This paper's main result presents a $3$-fold exponential algorithm that transforms a first-order formula $\varphi$ together with a number $d$ into a formula in Gaifman normal form that is equivalent to $\varphi$ on the class of structures of degree at most~$d$. For structures of polynomial growth, we even get a $2$-fold exponential algorithm. These results are complemented by matching lower bounds: We show that for structures of degree $2$, a $2$-fold exponential blow-up in the size of formulas cannot be avoided. And for structures of degree $3$, a $3$-fold exponential blow-up is unavoidable. As a result of independent interest we obtain a $1$-fold exponential algorithm which transforms a given first-order sentence~$\varphi$ of a very restricted shape into a sentence in Gaifman normal form that is equivalent to $\varphi$ on all structures.
11:0011:12Nathanaël Fijalkow and Charles Paperman On properties of logical sentences with arbitrary monadic predicates
SLIDES speaker: Charles Paperman

#### Abstract

In this talk, we introduce two properties for logical sentences using arbitrary numerical predicates: the Straubing property and the Crane Beach property. Both properties state that formulae defining simple languages do not need to use arbitrary complicated predicates, where simple either means regular or with a neutral letter. We restrict our attention to monadic predicates, and show that both properties hold in a strong syntactical sense.
11:1211:36Coffee break
11:3613:00Session 7
11:3611:48Mikołaj Bojańczyk, Bartek Klin, Sławomir Lasota and Szymon Toruńczyk Turing machines with atoms
SLIDES speaker: Bartek Klin

#### Abstract

We study Turing machines over sets with atoms, also known as nominal sets. Our main result is that deterministic machines are weaker than nondeterministic ones; in particular, P!=NP in sets with atoms. Our main construction is closely related to the Cai-Fuerer-Immerman graphs used in descriptive complexity theory.
11:4812:00Alexander Kurz, Tomoyuki Suzuki and Emilio Tuosto On regular expressions and nominal automata
SLIDES speaker: Tomoyuki Suzuki

#### Abstract

In several branches of computer sciences, automata are often used to describe computational behaviours. Among those developments, automata equipped with resource devices, e.g. a finite-memory or local registers, and languages over infinite alphabets are collecting more and more attentions. In this talk, we would like to discuss a possible general theory for those resource-handling automata from the point of nominal regular expressions. As already published works, we shall present the laywered-technique and the Kleene-style theorem. On top, as our ongoing work, by comparing possible actions (labels) on transitions, we will provide how those actions differentiate their language-recognisability and show the automata-hierarchy of languages over infinite alphabets.
12:0012:12Szymon Toruńczyk, Mikołaj Bojańczyk and Luc Segoufin Verification of database driven systems via amalgamation
SLIDES speaker: Szymon Torunczyk

#### Abstract

We describe a general framework for static verification of systems that base their decisions upon queries to databases. The database is specified using constraints, typically a schema, and is not modified during a run of the system. The system is equipped with a finite number of registers for storing intermediate information from the database and the specification consists of a transition table described using quantifier-free formulas that can query either the database or the registers. Our main result concerns systems querying XML databases -- modeled as data trees -- using quantifier-free formulas with predicates such as the descendant axis or comparison of data values. Our technique is based on the notion of amalgamation and is quite general. For instance it also applies to relational databases (with an optimal \pspace algorithm).
12:1212:24Thomas Colcombet and Amaldev Manuel μ-calculus on data words
SLIDES speaker: Amaldev Manuel

#### Abstract

We introduce and explore various fragments of μ-calculus on data words. We show that full μ-calculus is undecidable, but its ν-fragment is decidable by reduction to data automata. We disclose two subclasses of the ν-fragment that enjoy the further property of being closed under negation, namely the class of Bounded Reversal (BR) and the class of Bounded Mode Alternation (BMA). The latter is contained in the former class and is already sufficiently expressive for capturing several logics studied in the literature like $\fotwo$ and Data-LTL. We then characterize these two fragments as cascades of suitably defined transducer models. We finally prove the separation of BMA from BR using a novel paradigm of circuits and prove hierarchy theorems for BMA, Data-LTL and $\fotwo$.
12:2412:36Mikołaj Bojańczyk and Sławomir Lasota A machine-independent characterization of timed languages
SLIDES speaker: Slawomir Lasota

#### Abstract

We use a variant of sets with atoms (known also as nominal sets) as a framework suitable for stating and proving the following two results on timed automata. The first result is a machine-independent characterization of languages of deterministic timed automata, a la Myhill-Nerode Theorem. As our second result we define a class of automata that slightly extends timed automata and is effectively closed under minimization.
12:3612:48Daniel Bundala and Joël Ouaknine On the complexity of path checking in temporal logics
SLIDES speaker: Daniel Bundala

#### Abstract

Given a formula in a temporal logic such as LTL or MTL, a fundamental problem is the complexity of evaluating the formula on a given word. For LTL, the complexity of this task was recently shown to be in NC hierarchy. In this paper, we establish a connection between LTL path checking and planar circuits. We use the connection to show that the path-checking problem for LTL extended with exclusive or is already P-hard. We then present an NC algorithm for MTL, a quantitative (or metric) extension of LTL and give an AC-1 algorithm for UTL, the unary fragment of LTL.
12:4813:00Diego Figueira On XPath with transitive axes and data tests
SLIDES speaker: Diego Figueira

#### Abstract

We study the satisfiability problem for XPath with data equality tests. XPath is a node selecting language for XML documents whose satisfiability problem is known to be undecidable, even for very simple fragments. However, we show that the satisfiability for XPath with the rightward, leftward and downward reflexive-transitive axes (namely following- sibling-or-self, preceding-sibling-or-self, descendant-or-self) is decidable. Our algorithm yields a complexity of 3ExpSpace, and we also identify an expressive-equivalent normal form for the logic for which the satisfiability problem is in 2ExpSpace. These results are in contrast with the undecidability of the satisfiability problem as soon as we replace the reflexive-transitive axes with just transitive (non-reflexive) ones.
13:0014:30Lunch
14:3015:20Invited Talk
14:3015:20Marco Scarsini Invited talk: Existence of equilibria in countable games
SLIDES speaker: Marco Scarsini

#### Abstract

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Wald's pick-the-larger-integer game. Several authors have provided conditions for the existence of equilibria in infinite games. These conditions are typically of topological nature and are not applicable to countable games. Here we establish an existence result for the equilibrium of countable games when the strategy sets are a countable group and the payoffs are functions of the group operation. In order to obtain the existence of equilibria, finitely additive mixed strategies have to be allowed. This creates a problem of selection of a product measure of mixed strategies. We propose a family of such selections and prove existence of an equilibrium that does not depend on the selection. As a byproduct we show that if finitely additive mixed strategies are allowed, then Wald's game admits an equilibrium.
15:2015:30Break
15:3616:48Session 8
15:3615:48Stéphane Le Roux Infinite sequential Nash equilibrium
SLIDES speaker: Le Roux Stephane

#### Abstract

Borel determinacy says that all infinite-tree win-lose two-player games have a Nash equilibrium provided that the winning sets of the players are Borel. This talk generalises it and shows that all infinite-tree multi-outcome multi-player games have a Nash equilibrium provided that the outcome function is "Borel measurable" and that the player preferences have no infinite ascending chains. open access to the article at http://lmcs-online.org/ojs/viewarticle.php?id=985&layout=abstract&iid=39
15:4816:00Valentin Goranko, Wojtek Jamroga and Paolo Turrini Strategic games and truly playable effectivity functions
SLIDES speaker: Wojtek Jamroga

#### Abstract

A well-known result states that every strategic game generates a playable effectivity function, and every playable effectivity function can be implemented with a strategic game. We show that the latter does not hold for infinite games. We identify the error in the proof, and present examples of playable effectivity functions for which no equivalent strategic game exists. Then, we characterize the class of *truly playable* functions that do correspond to strategic games. We also show that Coalition Logic cannot distinguish between the two classes, and we extend it to a logic that is expressive enough.
16:0016:12Laurent Doyen and Marco Faella Best-effort control for Markov decision processes
SLIDES speaker: Marco Faella

#### Abstract

The premise of this talk is that in order to obtain realistic decision plans for Markov Decision Processes (or other decision-theoretic models) it is useful to consider solution concepts that are as discriminating as possible, by exploiting as much as possible the information provided in the model. Hence, we propose novel solution concepts for MDPs, obtained by lexicographically composing different risk attitudes, ranging from absolutely risk-averse, or pessimistic, to risk-seeking, or optimistic, in an order that depends on the application domain.
16:1216:24Krishnendu Chatterjee, Laurent Doyen, Mickael Randour and Jean-François Raskin Looking at mean-payoff and total-payoff through windows
SLIDES speaker: Mickael Randour

#### Abstract

We consider two-player games with mean-payoff (MP) and total-payoff (TP) objectives. In single dimension, their complexities coincide. In multi dimensions, MP games are coNP-complete. We show that TP games are undecidable. We introduce conservative approximations, considering the payoff over a local finite window sliding along a play. For single dimension, we show that (i) if the window is polynomial, deciding the winner is in P, and (ii) the existence of a bounded window can be decided in NP $\cap$ coNP, and is at least as hard as solving MP games. For multi dimensions, we show that (i) the fixed window size problem is EXP-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.
16:2416:36Martin Lang and Christof Löding Resource reachability games on pushdown graphs
SLIDES speaker: Martin Lang

#### Abstract

We consider two-player games on the configuration graph of pushdown systems with an additional finite set of non-negative integer counters. These counters can be incremented, reset to zero or left unchanged by the transition rules of the pushdown system. We associate the cost of a play with the highest counter value that occurs and look at a combined reachability and cost-limit winning condition. Is there a uniform cost-bound k such that one can win from a set of configurations A with this bound? We provide a solution to this question by an extension of the well-known saturation principle.
16:3616:48Marcus Gelderie Strategy composition in compositional games
SLIDES speaker: Marcus Gelderie

#### Abstract

When studying games played on finite arenas, the arena is given explicitly, hiding the underlying structure of the arena. We study games where the global arena is a product of several smaller, constituent arenas. We investigate how these "global games" can be solved by playing "component games" on the constituent arenas. To this end, we introduce two kinds of products of arenas. Moreover, we define a suitable notion of strategy composition and show how, for the first notion of product, winning strategies in reachability games can be composed from winning strategies in games on the constituent arenas. For the second kind of product, the complexity of solving the global game shows that a general composition theorem is equivalent to proving Pspace = Exptime.
16:4817:12Coffee Break
17:1218:36Session 9
17:1217:24Matteo Mio Game semantics for probabilistic mu-calculi
SLIDES speaker: Matteo Mio

#### Abstract

I will introduce a novel class of two-player games, called "Two-Player Stochastic meta-Parity Games", which are used in my PhD Thesis to give Game Semantics to expressive probabilistic-variants of the Modal mu-Calculus. This new class of games is proven to be "determined". I will discuss some of the technical aspects of the proof.
17:2417:36Olivier Finkel The determinacy of infinite games specified by automata
SLIDES speaker: Olivier Finkel

#### Abstract

We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter BŁchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption. Using some results of set theory we prove that one can effectively construct a 1-counter BŁchi automaton A such that: (1) There exists a model of ZFC in which Player 1 has a winning strategy in the Gale-Stewart game G(L(A)); but the winning strategies cannot be recursive and not even hyperarithmetical. (2) There exists a model of ZFC in which the Gale-Stewart game is not determined.
17:3617:48Alessandro Facchini, Michał Skrzypczak and Filip Murlak Game or not Game?
SLIDES speaker: Alessandro Facchini

#### Abstract

Recently the present authors have shown that both the non-deterministic and the alternating Rabin-Mostowski index problems are decidable for languages recognisable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition. In order to be able to claim decidability of the index problem for a given subclass of regular languages, one should however prove that membership in is decidable too. In this talk we show that membership in the class of languages recognizable by game automata is decidable.
17:4818:00Jacques Duparc and Yann Pequignot Playing reduction games on Scott domains
SLIDES speaker: Yann Pequignot

#### Abstract

If we take the complexity of a property to mean the difficulty of determining when it holds, 'simple reductions provide a way to organise properties in terms of their complexity. In a topological space, the notion of Wadge reducibility is obtained by interpreting 'simple as continuous. While on the Cantor space this gives a nice and useful hierarchy on the Borel sets, on the real line, for example, Wadge reducibility gives no hierarchy at all. We define a notion of reducibility for second countable T0 topological spaces, based on admissible representations, which always semi-wellorders the Borel sets.
18:0018:12Henryk Michalewski Regular languages of infinite trees of low Borel complexity
SLIDES speaker: Henryk Michalewski

#### Abstract

M. Bojanczyk and T. Place proved that for a regular language of infinite trees it is decidable if it is a boolean combination of open sets. The class of Delta^0_2 sets consists of sets which are simultaneously F_sigma and G_delta. Every boolean combination of open sets belongs to the class Delta^0_2. I will present a small modification of the result of M. Bojanczyk and T. Place. Namely, provide an algorithm to decide whether a given regular language of infinite trees belongs to the class \Delta^0_2.
18:1218:24Yde Venema Game bisimulations between basic positions
SLIDES speaker: Yde Venema

#### Abstract

Acceptance games and evaluation games provide examples of parity games in which some positions can be singled out as being *basic*, in the sense that (1) matches proceed in *rounds*, moving from one basic position to another, and (2) when determining the winner of an infinite match, only the basic positions matter. We introduce a notion of bisimulation between two such games that combines Pauly's bisimulation between extensive strategic games, with a combinatorial part for the parity condition. Applications include the proof of complementation lemmas in automata theory.
18:2418:36David Janin From strings to higher dimensional strings
SLIDES speaker: David Janin

#### Abstract

There are well-known connections between word language theory and semigroup theory, mediated by free monoids, with deep link with the theory of finite state automata. By considering free inverse monoids instead of free monoids and premorphisms into ordered monoids instead of morphisms into monoids, we manage to lift these connections to languages of finite trees and, beyond, towards a more general notion of higher dimensional strings. In this talk, we will give a quick overview of the background results with a special emphasis on the main underlying concepts and methods.

### Saturday 21 September

09:0009:50Invited Talk
09:0009:50Moshe Y. Vardi Invited Talk: The rise and fall of Linear Temporal Logic
SLIDES speaker: Moshe Y. Vardi

#### Abstract

One of the surprising developments in the area of program verification in the late part of the 20th Century is the emergence of Linear Temporal Logic (LTL), a logic that emerged in philisophical studies of free will, as the cannonical language for describing temporal behavior of computer systems. LTL, however, is not expressive enough for industrial applications. The first decade of the 21 Century saw the emergence of industrial temporal logics such as ForSpec, PSL, and SVA. These logics, however, are not clean enough to serve as objects of theoretical study. This talk will describe the rise and fall of LTL, and will propose a new cannonical temporal logic: Linear Dynamic Logic (LDL).
09:5010:00Break
10:0011:15Session 10A
10:0010:15Fabio Mogavero, Aniello Murano and Luigi Sauro On the boundary of behavioral strategies
SLIDES speaker: Aniello Murano

#### Abstract

In multi-agent games, a recent contribution is given by Strategy Logic (SL), a powerful formalism that allows to reason explicitly about strategies as first order objects. The price to pay for the high expressiveness of SL is that it admits non-behavioral strategies, i.e., a choice of an agent in a play may depend on choices made in another counterfactual play. As the latter moves are unpredictable, these strategies cannot be synthesized in practice. In this talk, we introduce two maximal syntactical fragments of SL admitting behavioral strategies only. As a consequence, we show that the model-checking problem for both fragments is solvable in 2EXPTIME, as it is for the subsumed ATL*.
10:1510:30Francois Laroussinie and Nicolas Markey Satisfiability of ATL with strategy contexts
SLIDES speaker: Nicolas Markey

#### Abstract

ATLsc is a powerful formalism for reasoning about multi-agent systems; it is a natural variant of the semantics of the logic ATL, as defined by Alur, Henzinger and Kupferman. Using a translation into QCTL (CTL extended with quantification over atomic propositions), we prove that ATLsc satisfiability is decidable when satisfiability is restricted to turn-based games, or when the set of moves allowed to the players in advance. On the other hand, when strategy quantification is restricted to memoryless strategies, satisfiability is undecidable in all considered cases.
10:3010:45Amélie David and Serenella Cerrito From ATL tableaux to alternating automata
SLIDES speaker: Amélie David

#### Abstract

In a global context of formal specification, a theoritecal question is : as for LTL, is it possible to construct an automaton from a tableau-based decision procedure for ATL (Alternating-time Temporal Logic)? To answer that question, we propose a new way of constructing a specific kind of alternating tree automaton, the so called joker automaton, from the construction of the tableau-based decision procedure for ATL [Goranko,Shkatov/2009]. This new automaton recognize all models of a formulae without restrictions on the moves of agents.
10:4511:00Francesco Belardinelli, Andrew Vaughan Jones and Alessio Lomuscio Model checking Temporal-Epistemic Logic using alternating tree automata
SLIDES speaker: Francesco Belardinelli

#### Abstract

We introduce a novel automata-theoretic approach for the verification of multi-agent systems. We present epistemic alternating tree automata, an extension of alternating tree automata, and use them to represent specifications in the temporal epistemic logic CTLK. We show that model check- ing a memory-less interpreted system against a CTLK prop- erty can be reduced to checking the language non-emptiness of the composition of two epistemic tree automata. We report on an experimental implementation and discuss preliminary results. We evaluate the effectiveness of the technique using two real-life scenarios: a gossip protocol and the train gate controller.
11:0011:15Rodica Bozianu, Cătălin Dima and Constantin Enea: The epistemic μ-calculus
SLIDES speaker: Catalin Dima

#### Abstract

We discuss expressivity issues concerning the epistemic mu-calculus with synchronous and perfect recall semantics w.r.t. games with partial observation, alternating temporal logics with incomplete observation, and an extension of the monadic second-order logic on trees.
10:0011:15Session 10B
10:0010:15Jakub Michaliszyn, Jan Otop and Emanuel Kieronski Elementary modal logics -- decidability and complexity
SLIDES speaker: Jakub Michaliszyn

#### Abstract

Modal logic is called "elementary" if it is considered over class of frames definable by a first-order formula. Different formulae lead to different logics, and many of them find their applications in computer science. The aim of the Highlights conference talk is to present a wide picture of the latest research on the satisfiability problem of elementary modal logics. The talk will provide all the necessarily definitions, discuss the motivation, summarise the recent research papers on this topic, and discuss some open problems.
10:1510:30Angelo Montanari and Pietro Sala Adding an equivalence relation to the interval logic complexity and expressiveness
SLIDES speaker: Pietro Sala

#### Abstract

We study the effects of the addition of an equivalence relation to one of the most representative interval temporal logics, namely, the logic ABBbar of Allen's relations "meets", "begun by", and "begins". We first prove that the satisfiability problem for the resulting logic ABBbar-sim remains decidable over finite linear orders, but it becomes nonprimitive recursive, while decidability is lost over $\bbN$. Then, we show that ABBbar-sim is expressive enough to define $\omega{S}$-regular languages.
10:3010:45Arthur Milchior Deciding in polynomial time whether a set recognized by an automaton is definable in FO[<,mod]
SLIDES speaker: Arthur Milchior

#### Abstract

In this talk, we are interested by expressivity of automaton reading a base b r-tuple of natural numbers. It is well known that those automaton recognize b-recognizable set. We will study how to decide, in polynomial time if the set recognized by an automaton is definable a smaller structure as \FO[+] or \FO[<,\moda], and how to compute a formula in this structure that accepts this set.
10:4511:00Dietrich Kuske Logical aspects of the lexicographic order on 1-counter languages
SLIDES speaker: Dietrich Kuske

#### Abstract

From Rabin's tree theorem, one can infer that the monadic second order theory of the lexicographic order on any regular language is decidable. The same holds for deterministic context-free languages since they belong to Caucal's hierarchy. When dropping determinism, not even the first-order theory remains decidable (\'Esik \& Carayol). This talk demonstrates that undecidability occurs already for \begin{itemize} \item small fragments of first-order logic and \item 1-counter automata that are very close to being deterministic. \end{itemize}
11:0011:15Thomas Colcombet Magnitude Monadic Logic over words and the use of relative internal set theory
SLIDES speaker: Thomas Colcombet

#### Abstract

Cost monadic logic extends monadic second-order logic with the ability to measure the cardinality of sets and comes with decision procedures for boundedness related questions. We provide new decidability results allowing the systematic investigation of questions involving “relative boundedness”. We first introduce a suitable logic, magnitude monadic logic. We then establish the decidability of this logic over finite words. We finally advocate that developing the proofs in the axiomatic system of “relative internal set theory”, a variant of nonstandard analysis, entails a significant simplification of the proofs.
11:1511:45Coffee break
11:4513:00Session 11A
11:4512:00Fabio Mogavero, Aniello Murano and Loredana Sorrentino On promptness in parity games
SLIDES speaker: Loredana Sorrentino

#### Abstract

In this paper, we make a general study of the concept of promptness in parity games that allows to put under a unique theoretical framework several of the cited variants along with new ones. Also, we describe simple polynomial reductions from all these conditions to either Buchi or parity games, which simplify all previous known procedures.
12:0012:15Nils Bulling and Valentin Goranko Combining quantitative and qualitative strategic reasoning in concurrent multi-player games
SLIDES speaker: Valentin Goranko

#### Abstract

We propose a logical modeling framework, combining a game-theoretic study of the abilities of players to achieve quantitative objectives in multi-player games (optimizing payoffs or preferences on outcomes) with a logical analysis of the abilities of players for achieving qualitative objectives (reaching or maintaining game states with desired properties). We enrich concurrent game models with payoffs for the normal form games associated with each state of the model and propose a quantitative extension of the logic ATL* enabling combination of quantitative and qualitative reasoning.
12:1512:30Alessio Lomuscio, Hongyang Qu and Franco Raimondi MCMAS: A model checker for the verification of multi-agent systems
SLIDES speaker: Alessio Lomuscio

#### Abstract

12:3012:45Romain Brenguier, Jean-François Raskin and Mathieu Sassolas The complexity of admissibility in omega-regular games
SLIDES speaker: Mathieu Sassolas

#### Abstract

11A-2-Sassolas.txt Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games played on graphs with omega-regular objectives. In this talk, we study the algorithmic properties of this concept for such games. We settle the exact complexity of natural decision problems on the set of strategies that survive iterated elimination of dominated strategies. As a byproduct of our construction, we obtain automata which recognize all the possible outcomes of such strategies.
12:4513:00Leander Tentrup A compositional proof rule for Coordination Logic
SLIDES speaker: Leander Tentrup

#### Abstract

We present the first proof system for Coordination Logic (CL). CL provides a logical representation for the distributed realizability problem and extends the game-based temporal logics with quantification over strategies under incomplete information. The proof system is based on a reduction from CL to its decidable fragment. We propose a compositional proof rule which splits a given CL formula into two parts, a decidable CL formula and another, simplified, CL formula. Applying the rule repeatedly transforms the original CL formula into a collection of decidable CL formulas. Our proof system is a complete framework for the synthesis of distributed systems.
11:4513:00Session 11B
11:4512:00Antoine Durand-Gasselin Is the generic algorithm for first-order model-checking automatic structures optimal ?
SLIDES speaker: Antoine Durand-Gasselin

#### Abstract

Automatic structures are relational structures whose domain can be presented as a regular language and predicates as synchronously regular relations. The main result on automatic structures is an explicit algorithm to build an automaton that accepts any first-order relation, relying on the correspondance between logical connectives and classical operations over automata. In general, building this automaton is non-elementary, but for some automatic structures with elementary first-order theory, we show that this construction has a complexity close to that of the logic.
12:0012:15Claudia Carapelle, Alexander Kartzow and Markus Lohrey Satisfiability of CTL* with constraints
SLIDES speaker: Claudia Carapelle

#### Abstract

CTL* formulas can be enriched to express relations between variables whose value can range in a chosen concrete domain. Chosen the appropriate domain one can express quantitative properties that ordinary CTL^* formulas can only approximate through abstraction. We can refer directly to concrete values and describe how they change in time. In this talk we show that satisfiability for CTL* with equality-, order-, and modulo- constraints over the Z is decidable
12:1512:30Tomáš Babiak, František Blahoudek, Mojmir Kretinsky and Jan Strejček Effective translation of LTL to deterministic Rabin automata: Beyond the (F,G)-fragment
SLIDES speaker: Jan Strejcek

#### Abstract

Some applications of linear temporal logic (LTL) require to translate formulae of the logic to deterministic omega-automata. There are currently two translators producing deterministic automata: ltl2dstar working for the whole LTL and Rabinizer applicable to LTL(F,G) which is the LTL fragment using only modalities F and G. We present a new translation to deterministic Rabin automata via alternating automata and deterministic transition-based generalized Rabin automata. Our translation applies to a fragment that is strictly larger than LTL(F,G). Experimental results show that our algorithm can produce significantly smaller automata compared to Rabinizer and ltl2dstar, especially for more complex LTL formulae.
12:3012:45Dominik D. Freydenberger and Timo Kötzing Fast learning of restricted regular expressions and DTDs
SLIDES speaker: Dominik D. Freydenberger

#### Abstract

We study the problem of generalizing from a finite sample to a language taken from a predefined language class. The two language classes we consider are generated by restricted regular expressions (CHAREs and SOREs) that have significance in the specification of XML documents. For each of the two language classes we give an efficient algorithm returning a minimal generalization from the given finite sample to an element of the fixed language class; such generalizations are called descriptive. In this sense, both our algorithms are optimal.
12:4513:00Rajeev Alur, Loris D'Antoni, Sumit Gulwani, Dileep Kini and Mahesh Viswanathan Automated grading of DFA constructions
SLIDES speaker: Loris D'Antoni

#### Abstract

One challenge in making online education more effective is to develop automatic grading software that can provide meaningful feedback. This paper provides a solution to automatic grading of the standard computation-theory problem that asks a student to construct a deterministic finite automaton from the given description of its language. We focus on how to assign partial grades for incorrect answers. We experimentally show that the tool is able to assign partial grades in a meaningful way, and should be preferred over the human graders for both scalability and consistency.
13:0014:00Lunch
14:0015:15Session 12A
14:0014:15Loris D'Antoni and Rajeev Alur Streaming tree transducers
SLIDES speaker: Loris D'Antoni

#### Abstract

We introduce streaming tree transducers as an analyzable, executable, and expressive model for transforming unranked ordered trees. Given a linear encoding of the input tree, the transducer makes a single left-to-right pass through the input, and computes the output using a finite-state control, a visibly pushdown stack, and a finite set of variables storing output chunks that can be combined using concatenation and insertion. We prove the model to be equivalent to monadic second-order logic transductions. We show complexity bounds of ExpTime for type-checking and NExpTime for equivalence.
14:1514:30Emmanuel Filiot, Olivier Gauwin, Pierre-Alain Reynier and Frédéric Servais From two-way to one-way finite state transducers
SLIDES speaker: Emmanuel Filiot

#### Abstract

Any two-way finite state automaton is equivalent to some one-way finite state automaton. This well-known result, shown by Rabin and Scott and independently by Shepherdson, states that two-way finite state automata (even non-deterministic) characterize the class of regular languages. It is also known that this result does not extend to finite string transductions: (deterministic) two-way finite state transducers strictly extend the expressive power of (functional) one-way transducers. In particular deterministic two-way transducers capture exactly the class of MSO-transductions of finite strings. In this talk, we address the following definability problem: given a function defined by a two-way finite state transducer, is it definable by a one-way finite state transducer? By extending Rabin and Scott's proof to transductions, we show that this problem is decidable. Our procedure builds a one-way transducer, which is equivalent to the two-way transducer, whenever one exists.
14:3014:45Inès Klimann Automaton semigroups: the two-state case
SLIDES speaker: Klimann Ines

#### Abstract

A Mealy automaton is a deterministic, complete, letter-by-letter transducer, with same input and output alphabet. We can consider the semigroup generated by the functions on words induced by its states. We prove that semigroups generated by reversible two-state Mealy automata have remarkable growth properties: they are either finite or free. We give an effective procedure to decide finiteness or freeness of such semigroups when the generating automaton is also invertible.
14:4515:00Henryk Michalewski and Michał Skrzypczak Complexity collapse for unambiguous languages
SLIDES speaker: Michał Skrzypczak

#### Abstract

A nondeterministic automaton is unambiguous if it has at most one accepting run on every input. The class of languages recognisable by unambiguous tree automata is still not well-understood. In this paper we show the following complexity collapse: if A is an unambiguous Buchi tree automaton then L(A) is recognisable by a weak alternating automaton. We present also some extensions of this result. To our best knowledge this is the first parity index collapse that exploits unambiguity of an automaton.
15:0015:15Szczepan Hummel Unambiguity-preserving operation on tree languages that lifts topological complexity
SLIDES speaker: Szczepan Hummel

#### Abstract

We propose an operation on languages of infinite trees that significantly increases topological complexity but preserves unambiguity. We prove that iterating the operation yields topologically harder and harder sets. As an illustration, we might note that application of the operation to the empty language already produces a non-Borel set, and the next application of the operation produces a set that is outside the sigma-field generated by analytic sets. Moreover, we show how to perform a limit step of the iteration.
14:0015:15Session 12B
14:0014:15Can Bașkent What is game theoretical negation?

#### Abstract

In this talk, I will give a game semantics for a paraconsistent logic, and define a paraconsistent "win" - parallel to the paraconsistent understanding of truth.
14:1514:30Agnieszka Kulacka Expressive completeness of some logics
SLIDES speaker: Agnieszka Kulacka

#### Abstract

Expressive completeness, which is one of the themes in this field of research, compares the power of these logics to fragments of first-order logic over some class of frames. If logic is as expressive as first order logic, as logic US (with connectives Until, Since) is shown to be, it is as powerful as possible. It can express the same statements, but in a more concise and readable way. In this presentation I will show a method of proving expressive completeness of a temporal logic by the use of games. This will be demonstrated on example of a temporal logic with connectives Future and Past.
14:3014:45Claudia Carapelle, Shiguang Feng, Oliver Gil and Karin Quaas Ehrenfeucht-Fraisse games for Freeze LTL and Metric Temporal Logic over data words
SLIDES speaker: Shiguang Feng

#### Abstract

We consider TPTL(Z) and MTL(Z) whose semantics are based on nonmonotonic data words in which every point is assigned a natural number as its weight. We define a weighted version of the EF game on MTL. Using these games, we prove the following: 1. TPTL(Z) is strictly more expressive than MTL(Z). 2. The until hierarchy and the constant hierarchy are strict for MTL(Z). 3. It is undecidable whether a given TPTL(Z) formula can be expressed in MTL(Z).
14:4515:00Piotr Hofman, Richard Mayr and Patrick Totzke Decidability of weak simulation on one-counter nets
SLIDES speaker: Patrick Totzke

#### Abstract

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of one-counter automata with only a weak test for zero. We show that weak simulation preorder is decidable for OCN. In contrast, other semantic relations like weak bisimulation are undecidable for OCN, and so are weak (and strong) trace inclusion.
15:0015:15Piotr Hofman, Sławomir Lasota, Patrick Totzke and Richard Mayr Strong simulation for one counter nets is PSPACE-complete
SLIDES speaker: Piotrek Hofman

#### Abstract

A one counter net is a one counter automaton without possibility of testing 0 value. We proved that solving the simulation problem for one counter nets is P-SPACE complete.
15:1515:45Coffee break
15:4517:00Session 13A
15:4516:00Christian Eisentraut, Holger Hermanns, Johann Schuster, Andrea Turrini and Lijun Zhang The quest for minimal quotients for probabilistic automata
SLIDES speaker: Christian Eisentraut

#### Abstract

16:0016:15Nathanaël Fijalkow and Florian Horn We tried and we tried, and we applied and implied, and still probabilistic automata we could not decide!
SLIDES speaker:

#### Abstract

16:1516:30Parosh Aziz Abdulla, Richard Mayr, Arnaud Sangnier and Jeremy Sproston Solving parity games on integer vectors
SLIDES speaker: Arnaud Sangnier

#### Abstract

16:3016:45Maria Svorenova, Ivana Černá and Călin Belta Optimal control of MDPs with Temporal Logic constraints
SLIDES speaker: Maria Svorenova

#### Abstract

In this work, we focus on control of Markov decision processes with non-negative real-valued costs. We develop an algorithm to design a control strategy that guarantees the satisfaction of a correctness specification expressed as a formula of Linear Temporal Logic, while at the same time minimizing the expected average cost between two consecutive satisfactions of a desired property. The existing solutions to this problem in control theory are sub-optimal. By leveraging ideas from automata-based model checking and game theory, we provide an optimal solution.
16:4517:00Holger Hermanns, Jan Krčál and Jan Kretinsky Compositional verification and optimization of interactive Markov chains
SLIDES speaker: Jan Krčál

#### Abstract

We provide the first assume-guarantee reasoning for stochastic continuous-time systems. Interactive Markov chains (IMC) are compositional behavioural models similar to continuous-time Markov decision processes. Given a time-bounded property, an IMC component and a specification of the environment, we synthesize a scheduler optimizing the probability that the property is satisfied when the IMC is working in an unknown environment that satisfies the specification. In this talk we focus on a two-player continuous-time stochastic game model that we call controller-environment games that is the crucial step in the solution of the problem above.
15:4517:00Session 13B
15:4516:00Yde Venema Expressiveness modulo bisimilarity: a coalgebraic perspective
SLIDES speaker: Yde Venema

#### Abstract

Janin and Walukiewicz showed that the modal mu-calculus MC is the bisimulation-invariant fragment of monadic second-order logic MSO. Their proof uses parity automata with a transition map defined in terms of monadic first-order logic. We decompose their proof in three parts: (1) automata-theoretic characterizations of MSO and MC respectively, (2) a simple model-theoretic characterization of the identity-free fragment of monadic first-order logic, and (3) a coalgebraic result, stating that the second result propagates from the `one-step level' to the level of full fixpoint logics.
16:0016:15Joost Winter, Helle Hvid Hansen, Clemens Kupke and Jan Rutten A final coalgebra for k-regular and k-automatic sequences
SLIDES speaker: Joost Winter

#### Abstract

We offer a coalgebraic perspective on the k-regular sequences. For any k >= 1 and semiring S, the set of sequences with output in S is the carrier of a final coalgebra. This allows us to give a coalgebraic characterization of the k-regular sequences. Using an isomorphism based on a bijective numeration system, we thus obtain a structural correspondence between S-rational series over k nonterminals, and k-regular sequences with output in S. We will furthermore discuss a connection with sequences definable by divide and conquer recurrences.
16:1516:30Boris Düdder, Moritz Martens and Jakob Rehof: Combinatory Logic synthesis and alternation
SLIDES speaker: Boris Düdder

#### Abstract

We discuss complexity theoretic results in the context of Combinatory Logic Synthesis which is a new approach to component-based synthesis using type inhabitation. The complexity theoretic reductions behind these results establish explicit and effective connections between combinatory logic inhabitation and automata theoretic models, in the form of alternating tree automata and alternating space bounded Turing machines. These computational models that are commonly found in automata theoretic approaches are related to synthesis based on logics within the MSO family of logics.
16:3016:45Sophia Knight, Catuscia Palamidessi, Prakash Panangaden and Frank Valencia Spatial and epistemic modalities in constraint-based process calculi
SLIDES speaker: Sophia Knight

#### Abstract

We describe the role epistemic reasoning can play in concurrency theory. The idea of using modalities as programming constructs has been largely unexplored. We add epistemic and spatial modalities as part of the programming language, not just as part of the meta-language to reason about protocols. We introduce spatial and epistemic process calculi to reason about information and knowledge distributed among agents in a system. We give domain-theoretic structures to represent this information, operational and denotational means to reason about possibly infinite behavior, and compact versions of infinite objects to simulate public announcement.

## Location

Highlights 2013 will be held at Université Paris Diderot, mainly in the Buffon building at 15 Rue Hélène Brion, with some parallel sessions in the Halle aux Farines at 2 Rue Marguerite Duras.

View location in Google Maps and on campus plan.

## Accommodation

You can find a variety of hotels close to the workshop venue, in the neighbourhood of Bercy - Bibliotheque François Mitterand. We also recommed and the Quartier Latin (two stops on RER C) and the area of Bastille / Gare de Lyon (three stops on Metro 14).

For hotels in the Quartier Latin, you may refer to the list compiled by Institut Henri Poincaré.

## Directions

### By flight

• From Charles de Gaulle airport: take RER B "Paris par le train" to Saint-Michel Notre-Dame, then RER C to Bibliothèque François Mitterrand (with the same ticket). Take the South exit towards Grands Moulins.
• From Orly airport: take Orlyval to the station Antony of the RER B, then RER B to the Saint-Michel Notre-Dame, then RER C to Bibliothèque François Mitterrand. Take the South exit Grands Moulins.

### By train

• From Gare du Nord: take RER B (direction St Rémy de Chevreuse / Robinson to Les Halles, then line 14 to Bibliothèque François Mitterrand.
• From Gare de Lyon: take line 14 (direction Olympiades) to Bibliothèque François Mitterrand.
• From Gare de l’Est: take metro line 4 (direction Porte d’Orléans) to Châtelet, then line 14 (direction Olympiades) to Bibliothèque François Mitterrand.

Information about public transportation in Paris is available at the RATP site.


text:
# How a RAM disk saved my life

## I don’t want to duel that much

In the last few weeks, I have been risking my life in the corridors at work. I have fit coworkers with a good sense of balance. Here is a picture of the horrible situations I’ve found myself into :

(props to xkcd. It’s the greatest webcomic in the universe. read it regularly)

Some of the code I’m dealing with, though, is not bound by the CPU speed or the number of cores I can throw at it. In particular, the ant distpack-opt task of the Scala compiler, compiling and packaging the documentation, is very much limited by storage transfer speeds. I have state-of-the-art SSDs on some of my machines, but yet found myself frustrated and waiting in front of the machine way too often.

To be fair, as far as I’m concerned, once is too often. I’m not so good when standing on a rolling chair.

## The RAM disk solution and its imperfections

The obvious solution, then was to use a RAM disk : insane transfer speeds would definitely help me, right ? Except RAM disks have two well-known problems:

• a RAM disk is, fundamentally, a piece of storage — a partition — carved out of your existing RAM. Assuming you have enough of it, it’s very fun until you have no more power. Every time you shut down your machine, you need to transfer the content of your RAM to your hard drive. Every time there is a sudden power outage, you basically lose the whole partition.

• moreover, a RAM partition is inherently limited in size. More interestingly, that’s a hard limit. What happens when you overflow the size of that partition is — at least on Linux — a nightmare: because the partition is treated like a fixed storage device, not a piece of memory (that could overflow into swap), it basically blows up in your face when full.

## The solutions on a modern Arch

Thankfully, the tools to manage those two problems have come to maturity. At the time of this writing, my machines are running a Linux 3.8rc7 kernel on ArchLinux transitioned to systemd, and running RAM disks in that kind of environment is a breeze.

• Ulatencyd (ArchLinux doc) is a daemon that uses cgroups, a recent-ish feature of the Linux kernel that lets you constrain the amount of resources allocated to a process. It watches over your processes, and dynamically gives a fair amount of ressources to them. Every second, it looks for memory pressure, and either relieves it if possible, or kills the guilty party if necessary. We have all had to face the swap of death, that frightening moment when a memory-leaking process overflows into the disk at a scary rate, slowing down — nay, taking down — your entire system. Here, Ulatencyd helps you separate processes on your system into cgroups, that are resized dynamically, and handle memory situations in a simple & graceful by default but amazingly configurable fashion.

The Archlinux install is amazingly simple. Install the AUR package, and activate it the systemd way (systemctl enable ulatencyd.service) after (optionally) editing the configuration (/etc/ulatencyd/ulatencyd.conf) : the default maximal amount of physical memory given to a process is 70%, and since I have 16GB of RAM on all my machines (with a RAM disk moving between 3 and 5 GB), this limit is pretty safe.

An added benefit ? In the middle of a long compilation, my machine is entirely responsive. I may be waiting for the compiler, but I can still surf the Internet in the meantime.

• Anything-sync-daemon (ArchLinux doc) is a small daemon — in fact, a small bash script — that is aimed at hiding the management of the day-to-day life of a RAM disk from the user. It uses rsync to synchronize the contents of your RAM disk to disk priodically, alleviating the risks coming from the need for your RAM to be powered at all times. It creates the partitions in your RAM and fills them up at boot time, and shelves them at shutdown.

Again, the ArchLinux install is insanely simple. There is an AUR package, the activation is trivial with systemd (systemctl enable asd.service) and the configuration is also easy. I simply edited /etc/asd.conf and put the following directories under RAMDISK :

WHATTOSYNC=('/home/huitseeker/Scala' '/home/huitseeker/.eclipse' '/home/huitseeker/.m2' '/usr/share/eclipse' '/home/huitseeker/workspace' '/home/huitseeker/junit-workspace' '/usr/lib/jvm' '/home/huitseeker/runtime-EclipseApplicationwithEquinoxWeaving' '/home/huitseeker/.sbt' '/home/huitseeker/.ivy2')

This is more than you need to simply compile Scala. As you probably noticed, this means :

## The Results

For the distpack-opt target of the Scala compiler, I have tried this method with :

• a slow, 2010-top-of-the-line Lynnfield core iMac (configuration) with a very well-used, slow hard drive.

• a reasonable X220 Lenovo Thinkpad (config) with an i5-2540M and an SSD.

Both configurations run on full-disk-encrypted storage using LUKS (but AVX-accelerated) (which explains the bad baseline you’re going to see for that disk-bound compilation).

• The slow iMac went from 124 minutes for compilation to 27 minutes.
• The Lenovo went from 24 minutes to 8 minutes 30 seconds

Yay ! no more risking my life fencing in corridors any more !

1. huitseeker posted this


text:
## The Effects of Invertibility on the Representational Complexity of Encoders in Variational Autoencoders

29 Sept 2021, 00:35 (edited 16 Mar 2022)ICLR 2022 PosterReaders: Everyone
• Keywords: variational autoencoders, encoder, representational complexity, Langevin, invertibility, deep learning theory
• Abstract: Training and using modern neural-network based latent-variable generative models (like Variational Autoencoders) often require simultaneously training a generative direction along with an inferential (encoding) direction, which approximates the posterior distribution over the latent variables. Thus, the question arises: how complex does the inferential model need to be, in order to be able to accurately model the posterior distribution of a given generative model? In this paper, we identify an important property of the generative map impacting the required size of the encoder. We show that if the generative map is ``strongly invertible" (in a sense we suitably formalize), the inferential model need not be much more complex. Conversely, we prove that there exist non-invertible generative maps, for which the encoding direction needs to be exponentially larger (under standard assumptions in computational complexity). Importantly, we do not require the generative model to be layerwise invertible, which a lot of the related literature assumes and isn't satisfied by many architectures used in practice (e.g. convolution and pooling based networks). Thus, we provide theoretical support for the empirical wisdom that learning deep generative models is harder when data lies on a low-dimensional manifold.
• One-sentence Summary: VAEs with invertible mean map have small approximate encoders; non-invertible maps can result in large encoders.
16 Replies