text:
In [1]:
import spot
spot.setup(show_default='.bn')
from IPython.display import display

Stutter-invariant languages¶

A language $L$ is said to be stutter-invariant iff $\ell_0\ldots\ell_{i-1}\ell_i\ell_{i+1}\ldots\in L \iff \ell_0\ldots\ell_{i-1}\ell_i\ell_i\ell_{i+1}\ldots\in L$, i.e., if duplicating a letter in a word or removing a duplicated letter does not change the membership of that word to $L$. These languages are also called stutter-insensitive. We use the adjective sutter-sensitive to describe a language that is not stutter-invariant. Of course we can extend this vocabulary to LTL formulas or automata that represent stutter-invariant languages.

Stutter-invariant languages play an important role in model checking. When verifying a stutter-invariant specification against a system, we know that we have some freedom in how we discretize the time in the model: as long as we do not hide changes of model variables that are observed by the specification, we can merge multiple steps of the model. This, combined by careful analysis of actions of the model that are independent, is the basis for a set of techniques known as partial-order reductions (POR) that postpone the visit of some successors in the model, because we know we can always visit them later.

Stutter-invariant formulas¶

When the specification is expressed as an LTL formula, a well known way to ensure it is stutter-invariant is to forbid the use of the X operator. Testing whether a formula is X-free can be done in constant time using the is_syntactic_stutter_invariant() method.

In [2]:
f = spot.formula('a U b')
print(f.is_syntactic_stutter_invariant())

True

In [3]:
f = spot.formula('a U Xb')
print(f.is_syntactic_stutter_invariant())

False

However some formula are syntactic-invariant despite their use of X. Spot implements some automaton-based check to detect stutter-invariance reliably and efficiently. This can be tested with the is_stutter_invariant() function.

In [4]:
g = spot.formula('F(a & X(!a & Gb))')
print(g.is_syntactic_stutter_invariant())
print(spot.is_stutter_invariant(g))

False
True

Of course this is_stutter_invariant() function first checks whether the formula is X-free before wasting time building automata, so if you want to detect stutter-invariant formulas in your model checker, this is the only function to use. Also, if you hapen to already have an automaton aut_g for g, you should pass it as a second argument to avoid it being recomputed: spot.is_stutter_invariant(g, aut_g).

It is also known that any stutter-invariant LTL formula can be converted to an X-free LTL formula. Several proofs of that exist. Spot implements the rewriting of K. Etessami under the name remove_x(). Note that the output of this function is only equivalent to its input if the latter is stutter-invariant.

In [5]:
spot.remove_x(g)

Out[5]:
$\mathsf{F} (a \land ((a \land (a \mathbin{\mathsf{U}} (\lnot a \land \mathsf{G} b)) \land ((\lnot b \mathbin{\mathsf{U}} \lnot a) \lor (b \mathbin{\mathsf{U}} \lnot a))) \lor (\lnot a \land (\lnot a \mathbin{\mathsf{U}} (a \land \lnot a \land \mathsf{G} b)) \land ((\lnot b \mathbin{\mathsf{U}} a) \lor (b \mathbin{\mathsf{U}} a))) \lor (b \land (b \mathbin{\mathsf{U}} (\lnot a \land \lnot b \land \mathsf{G} b)) \land ((\lnot a \mathbin{\mathsf{U}} \lnot b) \lor (a \mathbin{\mathsf{U}} \lnot b))) \lor (\lnot b \land (\lnot b \mathbin{\mathsf{U}} (\lnot a \land b \land \mathsf{G} b)) \land ((\lnot a \mathbin{\mathsf{U}} b) \lor (a \mathbin{\mathsf{U}} b))) \lor (\lnot a \land \mathsf{G} b \land (\mathsf{G} \lnot a \lor \mathsf{G} a) \land (\mathsf{G} b \lor \mathsf{G} \lnot b))))$

Stutter-invariant automata¶

Similarly to formulas, automata use a few bits to store some known properties about themselves, like whether they represent a stutter-invariant language. This property can be checked with the prop_stutter_invariant() method, but that returns a trival instance (i.e., yes, no, or maybe). Some algorithms will update that property whenever that is cheap or expliclitely asked for. For instance spot.translate() only sets the property if the translated formula is X-free.

In [6]:
aut = spot.translate(g)
print(aut.prop_stutter_invariant())

maybe

As suggested above, we can call is_stutter_invariant() by passing a formula and its automaton, to save on one translation. A second translation is still needed to complement the automaton.

In [7]:
print(spot.is_stutter_invariant(g, aut))

True

Note that prop_stutter_invariant() was updated as a side-effect so that any futher call to is_stutter_invariant() with this automaton will be instantaneous.

In [8]:
print(aut.prop_stutter_invariant())

yes

You have to be aware of this property being set in your back because if while playing with is_stutter_invariant() you the incorrect formula for an automaton by mistake, the automaton will have its property set incorrectly, and running is_stutter_inariant() with the correct formula will simply return the cached property.

In doubt, you can always reset the property as follows:

In [9]:
aut.prop_stutter_invariant(spot.trival_maybe())
print(aut.prop_stutter_invariant())

maybe

In case you have an automaton for which you do not have formula, you can also use is_stutter_invariant() by passing this automaton as the first argument. In that case a negated automaton will be constructed by determinization. If you do happen to have a negated automaton handy, you can pass it as a second argument to avoid that.

In [10]:
a1 = spot.automaton('''HOA: v1
AP: 1 "a"
States: 2
Start: 0
Acceptance: 0 t
--BODY--
State: 0 [0] 1
State: 1 [t] 0
--END--''')
display(a1)
print(spot.is_stutter_invariant(a1))

False

Explaining why a formula is not sutter-invariant¶

As explained in our Spin'15 paper the sutter-invariant checks are implemented using simple operators suchs as spot.closure(aut), that augment the language of L by adding words that can be obtained by removing duplicated letters, and spot.sl(aut) or spot.sl2(aut) that both augment the language that L by adding words that can be obtained by duplicating letters. The default is_stutter_invariant() function is implemented as spot.product(spot.closure(aut), spot.closure(neg_aut)).is_empty(), but that is just one possible implementation selected because it was more efficient.

Using these bricks, we can modify the original algorithm so it uses a counterexample to explain why a formula is stutter-sensitive.

In [11]:
def explain_stut(f):
f = spot.formula(f)
pos = spot.translate(f)
neg = spot.translate(spot.formula.Not(f))
word = spot.product(spot.closure(pos), spot.closure(neg)).accepting_word()
if word is None:
print(f, "is stutter invariant")
return
word.simplify()
word.use_all_aps(pos.ap_vars())
waut = word.as_automaton()
if waut.intersects(pos):
acc, rej, aut = "accepted", "rejected", neg
else:
acc, rej, aut = "rejected", "accepted", pos
word2 = spot.sl2(waut).intersecting_word(aut)
word2.simplify()
print("""{} is {} by {}
but if we stutter some of its letters, we get
{} which is {} by {}""".format(word, acc, f, word2, rej, f))

In [12]:
explain_stut('GF(a & Xb)')

cycle{!a & !b; a & b} is rejected by GF(a & Xb)
but if we stutter some of its letters, we get
cycle{!a & !b; a & b; a & b} which is accepted by GF(a & Xb)

Note that a variant of the above explanation procedure is already integerated in our on-line LTL translator tool (use the study tab).

Detecting stutter-invariant states¶

Even if the language of an automaton is not sutter invariant, some of its states may recognize a stutter-invariant language. (We assume the language of a state is the language the automaton would have when starting from this state.)

First example¶

For instance let us build a disjunction of a stutter-invariant formula and a stutter-sensitive one:

In [13]:
f1 = spot.formula('F(a & X!a & XF(b & X!b & Ga))')
f2 = spot.formula('F(a & Xa & XXa & G!b)')
f = spot.formula.Or([f1, f2])

print(spot.is_stutter_invariant(f1))
print(spot.is_stutter_invariant(f2))
print(spot.is_stutter_invariant(f))

True
False
False

In [14]:
pos = spot.translate(f)
display(pos)

While the automaton as a whole is stutter-sensitive, we can see that eventually we will enter a sub-automaton that is stutter-invariant.

The stutter_invariant_states() function returns a Boolean vector indiced by the state number. A state is marked as True if either its language is stutter-invariant, or if it can only be reached via a stutter-invariant state (see the second example later). As always, the second argument, f, can be omitted (pass None) if the formula is unknown, or it can be replaced by a negated automaton if it is known.

In [15]:
spot.stutter_invariant_states(pos, f)

Out[15]:
(False, True, False, True, True, True, True, True)

For convenience, the highligh_...() version colors the stutter-invariant states of the automaton for display. (That 5 is the color number for red in Spot's hard-coded palette.)

In [16]:
spot.highlight_stutter_invariant_states(pos, f, 5)
display(pos)

Such a procedure gives us a map of where POR can be enabled when model checking using this automaton.

Second example¶

This second example illustrates the fact that a state can be marked if it it not sutter-invariant but appear below a stutter-invariant state. We build our example automaton as the disjuction of the following two stutter-sensitive formulas, whose union is equivalent to the sutter-invariant formula GF!a.

In [17]:
g1 = spot.formula('GF(a & Xa) & GF!a')
g2 = spot.formula('!GF(a & Xa) & GF!a')
g = spot.formula.Or([g1, g2])

In [18]:
print(spot.is_stutter_invariant(g1))
print(spot.is_stutter_invariant(g2))
print(spot.is_stutter_invariant(g))

False
False
True

Here are the automata for g1 and g2, note that none of the states are stutter-invariant.

In [19]:
aut1 = spot.translate(g1)
aut1.set_name(str(g1))
spot.highlight_stutter_invariant_states(aut1, g1, 5)
display(aut1)

aut2 = spot.translate(g2)
aut2.set_name(str(g2))
spot.highlight_stutter_invariant_states(aut2, g2, 5)
display(aut2)

Now we build the sum of these two automata. The stutter-invariance check detects that the initial state is stutter-invariant (i.e., the entire language is stutter-invariant) so all states below it are marked despite the fact that the language recognized from these individual states would not be stutter-invariant.

In [20]:
aut = spot.sum(aut1, aut2)
# At this point it is unknown if AUT is stutter-invariant
assert(aut.prop_stutter_invariant().is_maybe())
spot.highlight_stutter_invariant_states(aut, g, 5)
display(aut)
# The stutter_invariant property is set on AUT as a side effect
# of calling sutter_invariant_states() or any variant of it.
assert(aut.prop_stutter_invariant().is_true())

Third example¶

These procedures work regardless of the acceptance condition. Here is an example with co-Büchi acceptance.

In this case we do not even have a formula to pass as second argument, so the check will perform a complementation by determinization.

In [21]:
aut = spot.automaton('randaut --seed=30 -Q4 -A"Fin(0)" a |')
spot.highlight_stutter_invariant_states(aut, None, 5)
display(aut)

If the negated automaton is already known, it can be passed as second argument (instead of the positive formula) to avoid unnecessary work.

Sutter-invariance at the letter level¶

Instead of marking each state as stuttering or not, we can list the letters that we can stutter in each state. More precisely, a state $q$ is stutter-invariant for letter $a$ if the membership to $L(q)$ of any word starting with $a$ is preserved by the operations that duplicate letters or remove duplicates.

$(\ell_0\ldots\ell_{i-1}\ell_i\ell_{i+1}\ldots\in L(q) \land \ell_0=a) \iff (\ell_0\ldots\ell_{i-1}\ell_i\ell_i\ell_{i+1}\ldots\in L(q)\land \ell_0=a)$

Under this definition, we can also say that $q$ is stutter-invariant iff it is stutter-invariant for any letter.

For instance consider the following automaton, for which all words that start with $b$ are stutter invariant. The initial state may not be declared as stutter-invariant because of words that start with $\lnot b$.

In [22]:
f = spot.formula('(!b&Xa) | Gb')
pos = spot.translate(f)
spot.highlight_stutter_invariant_states(pos, f, 5)
display(pos)

The stutter_invariant_letters() functions returns a vector of BDDs indexed by state numbers. The BDD at index $q$ specifies all letters $\ell$ for which state $q$ would be stuttering. Note that if $q$ is stutter-invariant or reachable from a stutter-invariant state, the associated BDD will be bddtrue (printed as 1 below).

This interface is a bit inconveniant to use interactively, due to the fact that we need a spot.bdd_dict object to print a BDD.

In [23]:
sil_vec = spot.stutter_invariant_letters(pos, f)
for q in range(pos.num_states()):
print("sil_vec[{}] =".format(q), spot.bdd_format_formula(pos.get_dict(), sil_vec[q]))

sil_vec[0] = 1
sil_vec[1] = 1
sil_vec[2] = 1
sil_vec[3] = b

The set of stutter-invariant states is not always forward closed¶

Consider the following automaton, which is a variant of our second example above.

The language accepted from state (2) is !GF(a & Xa) & GF!a (this can be simplified to FG(!a | X!a)), while the language accepted from state (0) is GF(a & Xa) & GF!a. Therefore. the language accepted from state (5) is a & X(GF!a). Since this is equivalent to a & GF(!a) state (5) recognizes stutter-invariant language, but as we can see, it is not the case that all states below (5) are also marked. In fact, states (0) can also be reached via states (7) and (6), recognizing respectively (a & X(a & GF!a)) | (!a & X(!a & GF(a & Xa) & GF!a)) and !a & GF(a & Xa) & GF!a)), i.e., two stutter-sentive languages.

In [24]:
ex1 = spot.automaton("""HOA: v1
States: 8 Start: 7 AP: 1 "a" Acceptance: 2 (Inf(0)&Inf(1))
--BODY--
State: 0 [!0] 0 {1} [0] 0 [0] 1 {0}
State: 1 [0] 0 [0] 1 {0}
State: 2 [t] 2 [!0] 3 [0] 4
State: 3 [!0] 3 {0 1} [0] 4 {0 1}
State: 4 [!0] 3 {0 1}
State: 5 [0] 0 [0] 2
State: 6 [!0] 0
State: 7 [!0] 6 [0] 5
--END--""")
spot.highlight_stutter_invariant_states(ex1, None, 5)
display(ex1)

This situation can be tested with spot.is_stutter_invariant_forward_closed(). The function returns -1 if the successor of any stutter-invariant state is it is also a stutter-invariant state, otherwise it return the number of one stutter-sensitive state that has a stutter-invariant state as predecessor.

In [25]:
sistates = spot.stutter_invariant_states(ex1)
spot.is_stutter_invariant_forward_closed(ex1, sistates)

Out[25]:
0

In cases where we prefer to have a forward-closed set of stutter-invariant states, it is always possible to duplicate the problematic states. The make_stutter_invariant_foward_closed_inplace() modifies the automaton in place, and also returns an updated copie of the vector of stutter-invariant states.

In [26]:
sistates2 = spot.make_stutter_invariant_forward_closed_inplace(ex1, sistates)
spot.highlight_stutter_invariant_states(ex1, None, 5)
display(ex1)
print(sistates2)

(False, False, True, True, True, True, False, False, True, True)

Now, state 0 is no longuer a problem.

In [27]:
spot.is_stutter_invariant_forward_closed(ex1, sistates2)

Out[27]:
-1

Let's see how infrequently the set of stutter-invarant states is not closed.

In [28]:
import spot.gen as gen

In [29]:
# Let's consider the LTL formula from the following 5 sources,
# and restrict ourselves to formulas that are not stutter-invariant.
formulas = [ f for f in gen.ltl_patterns(gen.LTL_DAC_PATTERNS,
gen.LTL_EH_PATTERNS,
gen.LTL_P_PATTERNS,
gen.LTL_SB_PATTERNS)
if not f.is_syntactic_stutter_invariant() ]

aut_size = []
sistates_size = []
fwd_closed = []

fmt = "{:40.40} {:>6} {:>8} {:>10}"
print(fmt.format("formula", "states", "SIstates", "fwd_closed"))
for f in formulas:
s = f.to_str()
aut = spot.translate(f)
aut_size.append(aut.num_states())
sistates = spot.stutter_invariant_states(aut, f)
sisz = sum(sistates)
sistates_size.append(sisz)
fc = spot.is_stutter_invariant_forward_closed(aut, sistates) == -1
fwd_closed.append(fc)
print(fmt.format(s, aut.num_states(), sisz, fc))

formula                                  states SIstates fwd_closed
Fp0 -> (!p0 U (!p0 & p1 & X(!p0 U p2)))       3        2          1
Fp0 -> (!p1 U (p0 | (!p1 & p2 & X(!p1 U       4        3          1
G!p0 | (!p0 U ((p0 & Fp1) -> (!p1 U (!p1      4        2          1
G((p0 & Fp1) -> (!p2 U (p1 | (!p2 & p3 &      4        1          1
G(p0 -> (Fp1 -> (!p1 U (p2 | (!p1 & p3 &      3        0          1
F(p0 & XFp1) -> (!p0 U p2)                    3        2          1
Fp0 -> (!(!p0 & p1 & X(!p0 U (!p0 & p2))      4        3          1
G!p0 | (!p0 U (p0 & (F(p1 & XFp2) -> (!p      4        2          1
G((p0 & Fp1) -> (!(!p1 & p2 & X(!p1 U (!      4        1          1
G(p0 -> ((!(!p1 & p2 & X(!p1 U (!p1 & p3      3        0          1
G((p0 & XFp1) -> XF(p1 & Fp2))                4        0          1
Fp0 -> (((p1 & X(!p0 U p2)) -> X(!p0 U (      6        2          1
G(p0 -> G((p1 & XFp2) -> X(!p2 U (p2 & F      5        0          1
G((p0 & Fp1) -> (((p2 & X(!p1 U p3)) ->      10        2          1
G(p0 -> (((p1 & X(!p2 U p3)) -> X(!p2 U      10        0          1
G(p0 -> F(p1 & XFp2))                         4        0          1
Fp0 -> ((p1 -> (!p0 U (!p0 & p2 & X(!p0       4        1          1
G(p0 -> G(p1 -> (p2 & XFp3)))                 3        3          1
G((p0 & Fp1) -> ((p2 -> (!p1 U (!p1 & p3      4        0          1
G(p0 -> ((p1 -> (!p2 U (!p2 & p3 & X(!p2      6        2          1
G(p0 -> F(p1 & !p2 & X(!p2 U p3)))            4        0          1
Fp0 -> ((p1 -> (!p0 U (!p0 & p2 & !p3 &       4        1          1
G(p0 -> G(p1 -> (p2 & !p3 & X(!p3 U p4))      3        3          1
G((p0 & Fp1) -> ((p2 -> (!p1 U (!p1 & p3      4        0          1
G(p0 -> ((p1 -> (!p2 U (!p2 & p3 & !p4 &      6        2          1
p0 U (p1 & X(p2 U p3))                        3        2          1
p0 U (p1 & X(p2 & F(p3 & XF(p4 & XF(p5 &      7        2          1
F(p0 & XGp1)                                  2        2          1
F(p0 & X(p1 & XFp2))                          4        2          1
F(p0 & X(p1 U p2))                            3        1          1
G(p0 & XF(p1 & XF(p2 & XFp3)))                1        1          1
GF(!(p1 <-> Xp1) | !(p0 <-> Xp0))             4        4          1
GF(!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2       9        9          1
G((p0 & p1 & !p2 & Xp2) -> X(p3 | X(!p1       3        0          1
G((p0 & p1 & !p2 & Xp2) -> X(X!p1 | (p2       5        5          1
G(p0 & p1 & !p2 & Xp2) -> X(X!p1 | (p2 U      1        1          1
G((!p0 & p1) -> Xp2)                          2        0          1
G(p0 -> X(p0 | p1))                           2        2          1
G((!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2      34       34          1
G((p0 & !p1 & Xp1 & Xp0) -> (p2 -> Xp3))      2        2          1
G(p0 -> X(!p0 U p1))                          2        0          1
G((!p0 & Xp0) -> X((p0 U p1) | Gp0))          3        3          1
G((!p0 & Xp0) -> X(p0 U (p0 & !p1 & X(p0      4        4          1
G((!p0 & Xp0) -> X(p0 U (p0 & !p1 & X(p0      6        6          1
G((p0 & X!p0) -> X(!p0 U (!p0 & !p1 & X(      6        6          1
G((p0 & X!p0) -> X(!p0 U (!p0 & !p1 & X(      8        8          1
G((!p0 & Xp0) -> X(!(!p0 & Xp0) U (!p1 &      6        6          1
G(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 |      12        0          1
G((Xp0 -> p0) -> (p1 <-> Xp1))                4        4          1
G((Xp0 -> p0) -> ((p1 -> Xp1) & (!p1 ->       4        4          1
p0 & XG!p0                                    2        1          1
XG(p0 -> (G!p1 | (!Xp1 U p2)))                4        1          1
XG((p0 & !p1) -> (G!p1 | (!p1 U p2)))         3        2          1
XG((p0 & p1) -> (Gp1 | (p1 U p2)))            3        2          1
Xp0 & G((!p0 & Xp0) -> XXp0)                  5        0          1
(Xp0 U Xp1) | !X(p0 U p1)                     1        1          1
(Xp0 U p1) | !X(p0 U (p0 & p1))               1        1          1
((Xp0 U p1) | !X(p0 U (p0 & p1))) & G(p0      2        2          1
((Xp0 U Xp1) | !X(p0 U p1)) & G(p0 -> Fp      2        2          1
!G(p0 -> X(p1 R p2))                          3        1          1
(p0 & Xp1) R X(((p2 U p3) R p0) U (p2 R       5        3          1
G(p0 | XGp1) & G(p2 | XG!p1)                  3        2          1
G(p0 | (Xp1 & X!p1))                          1        1          1

There is no instance of set of stutter-invariant states that is not closed in these example formulas.

In [30]:
sum(fwd_closed), len(fwd_closed)

Out[30]:
(63, 63)

Here is the percentage of stutter-invarant states.

In [31]:
100*sum(sistates_size)/sum(aut_size)

Out[31]:
55.78947368421053


text:
DEPRECATION WARNING

This documentation is not using the current rendering mechanism and will be deleted by December 31st, 2020. The extension maintainer should switch to the new system. Details on how to use the rendering mechanism can be found here.

# Breaking: Removal of partner extension Stuff¶

See :issue:

## Description¶

The extension tx_partner got its last update mid 2009 and is not compatible with any current TYPO3 LTS version. To clean up the code base, every usage and mention of the extension (and corresponding follow ups) were removed.

## Impact¶

Functions that rely on tx_partner are removed and will not work any more.

## Affected Installations¶

Any installations using functions of tx_partner.

## Migration¶

Nothing to migrate, the functiona are gone and needed to redone if needed.

format: plain


text:
Danger

This version of the Defining Custom Workloads page is kept here to document some of the legacy workload configurations still present in deploy/workloads/. New workloads should NOT be generated using these instructions. New workloads should be written by following the current version of the Defining Custom Workloads page.

Workloads in FireSim consist of a series of Jobs that are assigned to be run on individual simulations. Currently, we require that a Workload defines either:

• A single type of job, that is run on as many simulations as specfied by the user. These workloads are usually suffixed with -uniform, which indicates that all nodes in the workload run the same job. An example of such a workload is firesim/deploy/workloads/linux-uniform.json.
• Several different jobs, in which case there must be exactly as many jobs as there are running simulated nodes. An example of such a workload is firesim/deploy/workloads/ping-latency.json.

FireSim can take these workload definitions and perform two functions:

• Building workloads using firesim/deploy/workloads/gen-benchmark-rootfs.py
• Deploying workloads using the manager

In the following subsections, we will go through the two aforementioned example workload configurations, describing how these two functions use each part of the json file inline.

ERRATA: You will notice in the following json files the field “workloads” this should really be named “jobs” – we will fix this in a future release.

ERRATA: The following instructions assume the default buildroot-based linux distribution (br-base). In order to customize Fedora, you should build the basic Fedora image (as described in Running Fedora on FireSim) and modify the image directly (or in QEMU). Imporantly, Fedora currently does not support the “command” option for workloads.

firesim/deploy/workloads/linux-uniform.json is an example of a “uniform” style workload, where each simulated node runs the same software configuration.

Let’s take a look at this file:

{
"benchmark_name"            : "linux-uniform",
"common_bootbinary"         : "br-base-bin",
"common_rootfs"             : "br-base.img",
"common_outputs"            : ["/etc/os-release"],
"common_simulation_outputs" : ["uartlog", "memory_stats*.csv"]
}

There is also a corresponding directory named after this workload/file:

centos@ip-172-30-2-111.us-west-2.compute.internal:~/firesim-new/deploy/workloads/linux-uniform$ls -la total 4 drwxrwxr-x 2 centos centos 42 May 17 21:58 . drwxrwxr-x 13 centos centos 4096 May 18 17:14 .. lrwxrwxrwx 1 centos centos 41 May 17 21:58 br-base-bin -> ../../../sw/firesim-software/images/br-base-bin lrwxrwxrwx 1 centos centos 41 May 17 21:58 br-base.img -> ../../../sw/firesim-software/images/br-base.img  We will elaborate on this later. Looking at the JSON file, you’ll notice that this is a relatively simple workload definition. In this “uniform” case, the manager will name simulations after the benchmark_name field, appending a number for each simulation using the workload (e.g. linux-uniform0, linux-uniform1, and so on). It is standard pratice to keep benchmark_name, the json filename, and the above directory name the same. In this case, we have set all of them to linux-uniform. Next, the common_bootbinary field represents the binary that the simulations in this workload are expected to boot from. The manager will copy this binary for each of the nodes in the simulation (each gets its own copy). The common_bootbinary path is relative to the workload’s directory, in this case firesim/deploy/workloads/linux-uniform. You’ll notice in the above output from ls -la that this is actually just a symlink to br-base-bin that is built by the FireMarshal tool. Similarly, the common_rootfs field represents the disk image that the simulations in this workload are expected to boot from. The manager will copy this root filesystem image for each of the nodes in the simulation (each gets its own copy). The common_rootfs path is relative to the workload’s directory, in this case firesim/deploy/workloads/linux-uniform. You’ll notice in the above output from ls -la that this is actually just a symlink to br-base.img that is built by the FireMarshal tool. The common_outputs field is a list of outputs that the manager will copy out of the root filesystem image AFTER a simulation completes. In this simple example, when a workload running on a simulated cluster with firesim runworkload completes, /etc/os-release will be copied out from each rootfs and placed in the job’s output directory within the workload’s output directory (See the firesim runworkload section). You can add multiple paths here. The common_simulation_outputs field is a list of outputs that the manager will copy off of the simulation host machine AFTER a simulation completes. In this example, when a workload running on a simulated cluster with firesim runworkload completes, the uartlog (an automatically generated file that contains the full console output of the simulated system) and memory_stats.csv files will be copied out of the simulation’s base directory on the host instance and placed in the job’s output directory within the workload’s output directory (see the firesim runworkload section). You can add multiple paths here. ERRATA: “Uniform” style workloads currently do not support being automatically built – you can currently hack around this by building the rootfs as a single-node non-uniform workload, then deleting the workloads field of the JSON to make the manager treat it as a uniform workload. This will be fixed in a future release. ## Non-uniform Workload JSON (explicit job per simulated node)¶ Now, we’ll look at the ping-latency workload, which explicitly defines a job per simulated node. { "common_bootbinary" : "bbl-vmlinux", "benchmark_name" : "ping-latency", "deliver_dir" : "/", "common_args" : [], "common_files" : ["bin/pinglatency.sh"], "common_outputs" : [], "common_simulation_outputs" : ["uartlog"], "no_post_run_hook": "", "workloads" : [ { "name": "pinger", "files": [], "command": "pinglatency.sh && poweroff -f", "simulation_outputs": [], "outputs": [] }, { "name": "pingee", "files": [], "command": "while true; do sleep 1000; done", "simulation_outputs": [], "outputs": [] }, { "name": "idler-1", "files": [], "command": "while true; do sleep 1000; done", "simulation_outputs": [], "outputs": [] }, { "name": "idler-2", "files": [], "command": "while true; do sleep 1000; done", "simulation_outputs": [], "outputs": [] }, { "name": "idler-3", "files": [], "command": "while true; do sleep 1000; done", "simulation_outputs": [], "outputs": [] }, { "name": "idler-4", "files": [], "command": "while true; do sleep 1000; done", "simulation_outputs": [], "outputs": [] }, { "name": "idler-5", "files": [], "command": "while true; do sleep 1000; done", "simulation_outputs": [], "outputs": [] }, { "name": "idler-6", "files": [], "command": "while true; do sleep 1000; done", "simulation_outputs": [], "outputs": [] } ] }  Additionally, let’s take a look at the state of the ping-latency directory AFTER the workload is built: centos@ip-172-30-2-111.us-west-2.compute.internal:~/firesim-new/deploy/workloads/ping-latency$ ls -la
total 15203216
drwxrwxr-x  3 centos centos       4096 May 18 07:45 .
drwxrwxr-x 13 centos centos       4096 May 18 17:14 ..
lrwxrwxrwx  1 centos centos         41 May 17 21:58 bbl-vmlinux -> ../linux-uniform/br-base-bin
-rw-rw-r--  1 centos centos          7 May 17 21:58 .gitignore
-rw-r--r--  1 centos centos 1946009600 May 18 07:45 idler-1.ext2
-rw-r--r--  1 centos centos 1946009600 May 18 07:45 idler-2.ext2
-rw-r--r--  1 centos centos 1946009600 May 18 07:45 idler-3.ext2
-rw-r--r--  1 centos centos 1946009600 May 18 07:45 idler-4.ext2
-rw-r--r--  1 centos centos 1946009600 May 18 07:45 idler-5.ext2
-rw-r--r--  1 centos centos 1946009600 May 18 07:46 idler-6.ext2
drwxrwxr-x  3 centos centos         16 May 17 21:58 overlay
-rw-r--r--  1 centos centos 1946009600 May 18 07:44 pingee.ext2
-rw-r--r--  1 centos centos 1946009600 May 18 07:44 pinger.ext2
-rw-rw-r--  1 centos centos       2236 May 17 21:58 ping-latency-graph.py

First, let’s identify some of these files:

• bbl-vmlinux: Just like in the linux-uniform case, this workload just uses the default Linux binary generated in firesim-software. Note that it’s named differently here, but still symlinks to br-base-bin in linux-uniform.
• .gitignore: This just ignores the generated rootfses, which we’ll learn about below.
• idler-[1-6].ext2, pingee.ext2, pinger.ext2: These are rootfses that are generated from the json script above. We’ll learn how to do this shortly.

Additionally, let’s look at the overlay subdirectory:

centos@ip-172-30-2-111.us-west-2.compute.internal:~/firesim-new/deploy/workloads/ping-latency/overlay\$ ls -la */*
-rwxrwxr-x 1 centos centos 249 May 17 21:58 bin/pinglatency.sh

This is a file that’s actually committed to the repo, that runs the benchmark we want to run on one of our simulated systems. We’ll see how this is used soon.

Now, let’s take a look at how we got here. First, let’s review some of the new fields present in this JSON file:

• common_files: This is an array of files that will be included in ALL of the job rootfses when they’re built. This is relative to a path that we’ll pass to the script that generates rootfses.

• workloads: This time, you’ll notice that we have this array, which is populated by objects that represent individual jobs. Each job has some additional fields:

• name: In this case, jobs are each assigned a name manually. These names MUST BE UNIQUE within a particular workload.
• files: Just like common_files, but specific to this job.
• command: This is the command that will be run automatically immediately when the simulation running this job boots up. This is usually the command that starts the workload we want.
• simulation_outputs: Just like common_simulation_outputs, but specific to this job.
• outputs: Just like common_outputs, but specific to this job.

In this example, we specify one node that boots up and runs the pinglatency.sh benchmark, then powers off cleanly and 7 nodes that just idle waiting to be pinged.

Given this JSON description, our existing pinglatency.sh script in the overlay directory, and the base rootfses generated in firesim-software, the following command will automatically generate all of the rootfses that you see in the ping-latency directory.

[ from the workloads/ directory ]
./gen-benchmark-rootfs.py -w ping-latency.json -r -b ../../sw/firesim-software/images/br-base.img -s ping-latency/overlay

Notice that we tell this script where the json file lives, where the base rootfs image is, and where we expect to find files that we want to include in the generated disk images. This script will take care of the rest and we’ll end up with idler-[1-6].ext2, pingee.ext2, and pinger.ext2!

You’ll notice a Makefile in the workloads/ directory – it contains many similar commands for all of the workloads included with FireSim.

Once you generate the rootfses for this workload, you can run it with the manager by setting workload=ping-latency.json in config_runtime.ini. The manager will automatically look for the generated rootfses (based on workload and job names that it reads from the json) and distribute work appropriately.

Just like in the uniform case, it will copy back the results that we specify in the json file. We’ll end up with a directory in firesim/deploy/results-workload/ named after the workload name, with a subdirectory named after each job in the workload, which will contain the output files we want.


text:
8.10: Example

In this chapter and in Appendix W many graphs are given with a red or green rectangle giving the value of the different parameters for an α=60o blade and an internal friction angle φ=20o. The external friction angle is assumed to be δ=2/3·φ. Most graphs are dimensionless, but Figure 8-49, Figure 8-50, Figure 8-51 and Figure 8-52 are based on a compressive strength UCS=100 MPa, a blade width w=0.1 m and a layer thickness hi=0.1 m.

8.10.1. Step 1: Brittle Shear

The the shear angle β=43.3o, horizontal force coefficient λHF=1.912, the verticle force coefficient λVF=0.572 and the Esp/UCS ratio=0.669. This gives a horizontal force Fh=0.669 MN, a vertical force Fv=0.200 MN and a specific energy of Esp=66.9 MPa. These values are peak values, but for comparison reasons these values will be used.

8.10.2. Step 2: The Transition Brittle Shear/Brittle Tensile

The transitions brittle shear/brittle tensile occur for UCS/BTS=4.985 and UCS/BTS=11.75. This can also be written as BTS=0.085·UCS and BTS=0.2·UCS, so BTS=8.5 MPa and BTS=20 MPaBTS or UTS are considered positive numbers, while tensile strength is considered to be negative in this book.
This means that below the Lower Limit BTS=8.5 MPa brittle shear failure cannot exist, so there is always brittle tensile failure. Above the Upper Limit BTS=20 MPa brittle tensile failure cannot exist, so there is always brittle shear failure. In between, both can exist , even at the same time, according to Figure 8-19 the Chip Type. Figure 8-49 and Figure 8-50 show the horizontal and vertical cutting forces as a function of the tensile strength for the case considered. Interpolation curves are shown, simulating the simultaneous occurrence of brittle shear and brittle tensile failure according to the Chip Type. For this interpolation the following method is used:

First define a factor according to:

$\ \begin{array}{left}\text{BTS} < \text{LowerLimit BTS} &\Rightarrow \mathrm{f}=\mathrm{1}\\ \text{BTS} > \text{UpperLimit BTS}&\Rightarrow \mathrm{f}=\mathrm{0}\\ \text{BTS} > \mathrm{Lowerlimit BTS}\\ &\Rightarrow \mathrm{f}=\left(\frac{\text { Upperlimit BTS - BTS }}{\text { Upperlimit BTS - LowerLimit BTS }}\right)^\mathrm{p}\\ \text{BTS} < \text{UpperLimit BTS}\end{array}\tag{8-140}$

Now the resulting cutting forces can be determined with:

$\ \begin{array}{left}\mathrm{F}_{\mathrm{h}}=\mathrm{F}_{\mathrm{h}, \text { TearType }} \cdot \mathrm{f}+\mathrm{F}_{\mathrm{h}, \text { ShearType }} \cdot(\mathrm{1}-\mathrm{f})\\ \mathrm{F}_{\mathrm{v}}=\mathrm{F}_{\mathrm{v}, \text { TearType }} \cdot \mathrm{f}+\mathrm{F}_{\mathrm{v}, \text { ShearType }} \cdot(1-\mathrm{f})\end{array}\tag{8-141}$

The power used in Figure 8-49 and Figure 8-50 is p=1, a linear transition from tensile failure to shear failure, the Chip Type.

8.10.3. Step 3: Applying Tensile Strengths of -5 MPa, -10 MPa and -25 MPa

From Figure 8-49 and Figure 8-50 the horizontal and vertical peak forces can be determined. They are given in the following table. Between brackets estimated average values, based on a 60% ratio between average and peak values.

 Tensile Strength Fh (N) Fv (MN) Esp (MPa) Esp/UCS (%) -5 MPa 0.207 (0.124) 0.062 (0.037) 20.7 (12.4) 20.7 (12.4) -10 MPa 0.446 (0.268) 0.134 (0.080) 44.6 (26.8) 44.6 (26.8) -25 MPa 0.669 (0.401) 0.200 (0.120) 66.9 (40.1) 66.9 (40.1)

The UCS/BTS ratio of 10 matches the findings of Roxborough (1987) giving a specific energy of about 25% of the UCS value.

$\ \mathrm{E}_{\mathrm{sp}}=\mathrm{0 .2 5} \cdot \mathrm{U . C . S .}+\mathrm{0 .1 1}\tag{8-142}$

8.10: Example is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.


text:
Efficiency of McEliece cryptography (ciphertext expansion)

Most of the sources say McEliece has never gained acceptance because of its large size of private and public keys.

However I have never heard about the size (or length) of its ciphertext. ("Ciphertext expansion".) For example, McEliece offers the linear code of length 1024 and of dimension 524. That means a plaintext of length 524 will be encrypted to a ciphertext of length 1024 and then will be sent. Isn't is also an inefficiency?

migrated from security.stackexchange.comSep 7 '15 at 11:25

This question came from our site for information security professionals.

• you can do the encryption with McEliece indeed really fast. And indeed the ratio $\beta=n/k$ defines the ciphertext expansion you'll observe. IIRC this value usually is $1.25\leq \beta \leq 1.5$. The ciphertext is then of size $n$ and the input of size $k$. – SEJPM Sep 7 '15 at 12:27


text:
# Binomial Tree Python

height-balanced 9. Xgboost Partial Dependence Plot Python. Binomial and trinomial trees allow for 1 additional state at each time step. For your convenience, the code has been packaged up into archives of different formats. It can also be shown that the approach is equivalent to the explicit finite difference method for option pricing. Последние твиты от Green Tree Python man (@tree_python). INTRODUCTION. Python provides following built-in function to help you accomplish common programming tasks. For terminal stock price array, I have stepped down from InitialStock * u**(iSteps - i) for i going from zero to 2*iSteps+ 1. p - probability of occurence of each trial (e. In this example, we will show you how to read an XML file and print out its values, via Python xml. Symmetric random walk python. com Free Programming Books Disclaimer This is an uno cial free book created for educational purposes and is not a liated with o cial Algorithms group(s) or company(s). † The two nodes A and C, which bracket node B, are the destinations of the other two branches from node X. tree by one date and considering a 3-date pure discount bond will allow us to calculate more interest rates. how two option pricing models, the binomial tree and Black–Scholes models, can be implemented sion on a tree. We will begin our implementation of a binary heap with the constructor. python amazon-web-services apache facebook ajax. sangsulinamu alae / Under the Oak Tree. ✓ ● Can efficiently find the minimum element of each packet. A binomial tree of height 2 is formed from two binomial trees, each of height 1. A binary search tree is a binary tree in which the key values in the left node is less than the root and the key values in the right node is greater than the root. Samples are drawn from a binomial distribution with specified parameters, n trials and p probability of success where n an integer >= 0 and p is in the interval [0,1]. We then examine how to modify the binomial schemes so as to incorporate the discrete dividend feature, early exercise and call features. The factory maintains an ArrayList of all the TreeNode objects it creates and allows you to create, fetch, and delete TreeNodes in the binomial lattice. Gradient boosting produces an ensemble of decision trees that, on their own, are weak decision So let's start with a Gradient Boosting regression model that has just 1 estimator and a tree with a depth. Binomial Expansions on Python. from scipy. It may not call any helper functions. This course focuses on an alternative method of implementing a two-dimensional binomial tree compared to that given in the previous chapter for pricing American options. Assuming a two period binomial model and, estimating , we can infer that the stock can move in any of the following ways If the latter were to be true, we could only exercise the option in 1 out of the 3 possible end-states since both 95. This is a very basic question about Bayesian inference. Plotting these two values over time is known as building a binomial tree. Bacaan lanjut. Basically, all you should do is apply the proper packages and their functions and classes. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package 'python-scipy' has no installation candidate. Binomial and trinomial trees allow for 1 additional state at each time step. For terminal stock price array, I have stepped down from InitialStock * u**(iSteps - i) for i going from zero to 2*iSteps+ 1. In 1993, Professor Arnold G. Parse trees can be used to represent real-world constructions like sentences or mathematical Representing a sentence as a tree structure allows us to work with the individual parts of the. Helper data structure: Certain programming problems are easier to solve using multiple data structures. Binomial Distribution. Price an American Option Using the Cox-Ross-Rubinstein Binomial Pricing Model Open Live Script This example shows how to price an American put option with an exercise price of $50 that matures in 5 months. Binomial Options Pricing Model: Naïve Python Implementation. Binomial Tree blog | May 21, 2018 In this post I will present another simple option pricing model: the Cox-Ross-Rubinstein model, also known as the binomial tree model, which is a variation of the original Black-Scholes model that I will cover in my next post. the payoffs in case of an European Option. Python 3 This is a tutorial in Python3, but this chapter of our course is available in a version for Python 2. In our data, age doesn't. The problem with the traditional method of constructing the binomial tree for options pricing is that extra care must be taken to ensure that the right cells are picked up in the calculation. The species is native to New Guinea, some islands in Indonesia, and the Cape York Peninsula in Australia. The other binomial tree becomes a subtree off of the new root. Root node on unrooted trees? In bioinformatics, trees are the result of many analyses, such as phylogenetics or clustering. With the time between two trading events shrinking to zero, the evolution of the price converges weakly to a lognormal diffusion. Thus, if the stock price is S ocurrently, then at the next point of time its price will either be uS oor dS. For instance, in a 3-step binomial tree there are 4 final states of option prices. A Monte Carlo simulation would theoretically work, but is computationally inefficient. It can also be shown that the approach is equivalent to the explicit finite difference method for option pricing. Binomial Distribution. Pytorch is a Python package, it is used for natural language processing. Answer Key van, box, sun, tree, zebra, ant, car, dog, flag, jam. Bacaan lanjut. Find height of a binary tree 6 tahun yang lalu. tree by one date and considering a 3-date pure discount bond will allow us to calculate more interest rates. The binomial tree is a computational method for pricing options on securities. binomial_graph¶ binomial_graph (n, p, seed = None, directed = False) ¶ Returns a $$G_{n,p}$$ random graph, also known as an Erdős-Rényi graph or a binomial graph. You'll receive a free ebook to read, and upon posting. 2 Handling Missing Values 2. I want to infer the probabilities (px and py, respectively) of each occurring given X and Y. Binomial Options Pricing Model: Naïve Python Implementation. These examples are extracted from open source projects. the binomial tree at time t +¢t0. Python JavaScript C C++ Java Kotlin Swift C# DSA. In the first stages our model will be inaccurate, but as we add complexity the model will become more realistic. Binomial no Python: Precisamos importar o pacote "binom". com/padraic00/Binomial-Options-Pricing-Model/blob/master/BOPM. The implementation of a method is far simpler than the hedging argument. Python Quickstart. The % symbol in Python is called the Modulo Operator. user38310 user38310. In rule post- ch attribute test t (precondition) EE LEARNING 71 alternative tree a al. Binary numbers representation in Python: Here, we will learn how to work with the binary numbers, how to assign, conversion and bitwise operations on binary numbers?. This is a write-up about my Python program to price European and American Options using Binomial Option Pricing model. Merge two dictionaries using dict. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package 'python-scipy' has no installation candidate. 2) A binomial coefficient C(n, k) also gives the number of ways, disregarding order, that k objects can be chosen from among n objects; more formally, the number of k-element subsets (or k-combinations) of an n-element set. 2 Probability Theory – Terminology 3. It includes everything in Python 3. The price of the asset underlying the derivative (for instance the stock price in the case of a stock option) is assumed to follow an. Python source files (. She squatted on a tree stump and vomited water. The Python Tree. Plus, seeing a graph of your problem, as opposed to a bunch of equations and numbers on a sheet of paper, can help you see the problem more clearly. p - probability of occurence of each trial (e. It is so easy, quick and fun to use. Thus, it is better to download all the code into a local directory before running. This release adds support for native Python types in templates. Python - Binomial Distribution Last Updated: 16-07-2020 Binomial distribution is a probability distribution that summarises the likelihood that a variable will take one of two independent values under a given set of parameters. 6 and Python 3. the simpler binomial method and move onto the more complex Longstaff-Schwartz method. Parse trees can be used to represent real-world constructions like sentences or mathematical Representing a sentence as a tree structure allows us to work with the individual parts of the. toss of a coin, it will either be head or tails. Below is the list of most common binomial expressions. Binomial Tree Python. For example, the following figure shows two binomial trees of rank 2. We know from our traditional decision tree (in blue) that Feature 1 is the best feature for splitting, but Tree 1 cannot see Feature 1 so it is forced to go with Feature 2 (black and underlined). The spreadsheet also calculate the Greeks (Delta, Gamma and Theta). choose” chooses elements from arrays and constructs a new array. The decision tree classifier is the most popularly used supervised learning algorithm. Green Tree Python Life Span Most green tree pythons can be expected to live into their mid-teens with good. Comments 2 Comments. This way a binomial tree can be built for multiple periods. Binary Tree Structure -- a quick introduction to binary trees and the code that operates on them Section 2. While there are many different types of loops, almost each type of loop has the same basic function: iterating over data to analyze or manipulate it. 51 1 1 bronze badge$\endgroup$1. Start studying Binomial Trees. Tags: binary tree , class , python , trees. At all other points in the tree there is a. Graphical Educational content for Mathematics, Science, Computer Science. The corresponding Python implementation of tree reduction algorithm would look similarly to this: # Generate terminal nodes of binomial tree level = [] print ('Tree level %i' % n) for i in range (0, n+ 1): # Iterate through nodes # Instrument's price at the node pr = price * d ** i * u ** (n-i) # Option value at the node (depending on side). Below is a python implementation of. Binary ordered tree (Python recipe) by Foo Bear. Python 3 This is a tutorial in Python3, but this chapter of our course is available in a version for Python 2. csv', encoding=. py Tree / Forest A tree is an undirected graph which contains no cycles. It has three parameters: n - number of trials. Binomial data and statistics are presented to us daily. The following example shows how to train binomial and multinomial logistic regression models for binary classification with elastic net. Binomial no Python: Precisamos importar o pacote "binom". It returns the remainder of dividing the left hand operand by right hand operand. Algorithms in Python. This is the most uncomfortable/suspicious one-liner I have ever seen. Step 2: While there is a higher order binomial tree can be found, perform the following: (a) Find two meta-processors V i,V j in V that has the smallest sum of degree in G and can be constructed as a binomial tree. the payoffs in case of an European Option. the binomial tree at time t +¢t0. binomial tree can then be built. These methods provide a useful alternative to those (numerical or analytical) methods. † The two nodes A and C, which bracket node B, are the destinations of the other two branches from node X. Compute Stock Option price using Binomial Tree in Python. The binomial table has a series of mini-tables inside of it, one for each selected value of n. Decision tree python code sample. from scipy. Start studying Binomial Trees. Binomial and trinomial trees are very popular tools commonly used in practice to calculate prices and sensitivity parameters of derivatives while avoiding direct reference to the fundamental differential equations governing the price of the instrument. Even though they come from two unrelated snake families that live on opposite sides of the planet, each could easily be mistaken for the other. Is there an existing data structure which can be used as tree?. Base 64 Encoding. Each of these probabilities are:. and its convertable in python using Pandas library. At all other points in the tree there is a. In this article we showed how you can use Python's popular Scikit-Learn library to use decision trees for both classification and regression tasks. bogotobogo. +50% damage from -33% damage from. Priority queue and heap queue data structure. Parameter s (value of the regularization parameter used for predictions) is set to 0. A tree is said to be a binary tree if it has atmost two children. the simpler binomial method and move onto the more complex Longstaff-Schwartz method. In this article, I will talk about various concepts related to binomial option pricing model. R-tree Spatial Indexing with Python. Schlegel, H. Trie (Prefix Tree, 26-ary Tree) Radix Tree (Compact Trie) Ternary Search Tree (Trie with BST of children) B Trees; B+ Trees; Sorting ; Comparison Sorting. Python 3 Now Available! This is a Python 3 trinket. Python JavaScript C C++ Java Kotlin Swift C# DSA. I don't know what you mean by binomial tree, sorry.$\endgroup$– Ben Reiniger Apr 27 at 21:29. The binomial distribution model deals with finding the probability of success of an event which has only two possible outcomes in a series of experiments. The triangular array of binomial coefficients is called Pascal's triangle after the seventeenth-century French mathematician Blaise Pascal. Adults average between 4 and 6 feet, with males on the lower end of this scale and females on the upper end. Welcome To Banyan Tree Spa Your Sanctuary For The Senses.$100 USD in 3 days (1 Review) 0. Decision boundaries created by a decision tree classifier. This means that any two vertices of the graph are connected by exactly one simple path. Binomial Tree Python. The following python program uses python list to build a tree data structure. Simple Python Trees. (2) Define the function f by: f(n) = { 10, n = 2. # Python has many built in encodings for different languages, # and even the Caeser cipher is built in import codecs cipher_text = codecs. How it can be done in python. Application of Decision tree with Python Here we will use the sci-kit learn package to implement the decision tree. A tree python was a breed of snake native to the Serpent Hills. Binomial Option Pricing Model Calculator. Deriving the Binomial Tree Risk Neutral Probability and Delta Ophir Gottlieb 10/11/2007 1 Set Up Using risk neutral pricing theory and a simple one step binomial tree, we can derive the risk neutral measure for pricing. One of the most fundamental tools in programming is a loop. I am trying to compute the price of an option and the code below is based on a text that i found in one of the threads. I am looking for different methods using Python code to determine which features to leave in, and which features to drop, in one’s logistic regression model. Rhino Developer. Example n = 5, k = 2 10. Trie (Prefix Tree, 26-ary Tree) Radix Tree (Compact Trie) Ternary Search Tree (Trie with BST of children) B Trees; B+ Trees; Sorting ; Comparison Sorting. com Free Programming Books Disclaimer This is an uno cial free book created for educational purposes and is not a liated with o cial Algorithms group(s) or company(s). Example: ${10 \choose 6} = \frac{10!}{6!4!} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 4 \times 3 \times 2 \times 1} = \frac{10 \times 9 \times 8 \times 7 }{4 \times 3 \times 2 \times 1} = \frac{5040}{24} = 210$. When visualizing a Bernoulli process, it is common to use a binary tree diagram in order to show the […] A Bernoulli process is a sequence of Bernoulli trials (the realization of n binary random variables), taking two values (0/1, Heads/Tails, Boy/Girl, etc…). In our data, age doesn't. Below is the list of most common binomial expressions. ” The null and alternative hypotheses for our test are as follows:. 1 by default, but needs to be tuned by the user. Python JavaScript C C++ Java Kotlin Swift C# DSA. This is a very basic question about Bayesian inference. This video gives a brief introduction on discrete binomial distribution. For example, the order 3 binomial tree is connected to an order 2, 1, and 0 (highlighted as blue, green and red respectively) binomial tree. February 18, 2013February 18, 2013kostas. In the tree above, each cell k is topping 2*k+1 and 2*k+2. You'll start to compile your tree in no time!. Decision Tree classifier implementation in Python with sklearn Library. 601 for illustration. com/Gewissta/Tree_based_algorithms_in_R_and_Python/master/Trees/credit_train. or precondi- iiven the above te preconditions ichever of these accuracy, then ep. Python has several functions for creating, reading, updating, and deleting files. In 1993, Professor Arnold G. One important assumption of Rubinstein’s original implied binomial tree is that all paths that lead to the same ending node have the same risk-neutral probability. (Python viridis, p. Python Input Output Import. 1 Lattice tree methods We start this section by revisiting the binomial model and consider its con-tinuous limits. Problem Solution 1. It has three parameters: n - number of trials. Luckily, we have the binomial theorem to solve the large power expression by putting values in the formula and expand it properly. Symmetric random walk python. Binomial Option pricing model is an important topic as far as FRM Part 1 exam is concerned. A Binary tree is a widely used tree data structure. Binomial Tree: A graphical representation of possible intrinsic values that an option may take at different nodes or time periods. Care and Breeding Green Tree Pythons Details the neonatal care and feeding of chrondro pythons in captivity, by Dr. In this post, we will use QuantLib and the Python extension to illustrate a very simple example. This is the most uncomfortable/suspicious one-liner I have ever seen. Dot Net Technologies. Introduction to Option Pricing with Binomial Trees This section will consider the pricing of a vanilla option using a Binomial Tree. Binomial Trees. Xbar Chart Python. In our data, age doesn't. $\begingroup$ The tree method is not exported to Python. Kluge published a detailed phylogenetic analysis that found that the green tree python was nested within the genus Morelia and most closely related to the rough-scaled python ( M. Having written about pricing American-style options on a binomial tree in q, I thought it would be instructive to do the same in Python and NumPy. Python's license is administered by the Python Software Foundation. Satchidanand Haridas. Decision Trees (DTs) are a non-parametric supervised learning method used for classification and For instance, in the example below, decision trees learn from data to approximate a sine curve with a. Submitted by Anuj Singh, on July 09, 2020 A binomial experiment is described by the following characteristics: An experiment that involves repeated trials. This book details the steps needed to retrieve time series data from different public data sources. (A+X) n = n C 0 A n X 0 + n C 1 A n-1 X 1 + n C 2 A n-2 X 2 +…. Basic knowledge of operating Computer , Basic Hello Dear Student , First of all , Welcome to the Python 3 Programming Course. i am a new member on this list. , Fonnesbeck C. Each TreeNode instance represents - you guessed it - a node in the binomial tree. Each of these probabilities are:. Python Data Types. The value at the leaves is easy to compute, since it is simply the exercise value. R-tree Spatial Indexing with Python. 1 of a tree 6. # Binomial Distribution in both "R"& "Python" explained with Example. Binary Tree Structure -- a quick introduction to binary trees and the code that operates on them Section 2. To get to the highest (110) or lowest (90) node of the final step of the tree requires, respectively, four stock up moves or four stock down moves. Binary Tree Problems -- practice problems in increasing order of difficulty Section 3. The Green Tree Python and Emerald Tree Boa - Care, Breeding and Natural History. Slide 14 Fig. Home » dictionary » Python » You are reading ». In the tree above, each cell k is topping 2*k+1 and 2*k+2. Python Quickstart. tags, or, preferably, tags. Binomial and trinomial trees allow for 1 additional state at each time step. It’s time to start implementing linear regression in Python. Each of these probabilities are:. The binomial tree B0 has one node. This is often known as the assumption of Binomial Path Independence (BPI). It can also be shown that the approach is equivalent to the explicit finite difference method for option pricing. The programming guide. leaf A bottom-most node in a tree, with no children. Cumulative Probability. It is important to have rules for naming species using binomial nomenclature (also called binomial, binominal or binary names) so that everyone does it in General Rules for Creating Binomial Names. The probability of finding exactly 3 heads in tossing a coin repeatedly for 10 times is estimated during the binomial distribution. I'm looking into getting a emerald tree boa or green tree python. For methods ‘complete’, ‘average’, ‘weighted’ and ‘ward’, an algorithm called nearest-neighbors chain is implemented. 99 are less than 97. In Python, the Dictionary class provides a function update() i. 1 Overview 3. With Cppsecret’s help and guidance along with Python – the most popular, versatile and flexible programming languages around today, you are guaranteed a future-ready, successful career in a market that is driven by consistent innovation and disruption. Can you please verify for yourself that your answer is still relevant? \$\endgroup\$ – Mast Aug 28 at 19:17. 7 and django and have confident to handle task with my previous knowladge. I have a small Python project on GitHub called inspect_word2vec that loads Google's model I had been using Python(x, y) to get a nice machine learning-oriented Python environment up and running. p - probability of occurence of each trial (e. the mean value of the binomial distribution) is. It's used to get the remainder of a division problem. Having said that, I think your answer may be misinformed due to those differences. Submitted by Anuj Singh, on July 09, 2020 A binomial experiment is described by the following characteristics: An experiment that involves repeated trials. The implementation of a method is far simpler than the hedging argument. ) from collections import defaultdict. 3 Exploration of Data using Visualization 3 Probability Distributions And Hypothesis Tests 3. Decision trees are supervised learning models used for problems involving classification and regression. I am looking for different methods using Python code to determine which features to leave in, and which features to drop, in one’s logistic regression model. Only RUB 220. Binomial and trinomial trees allow for 1 additional state at each time step. Binary numbers representation in Python: Here, we will learn how to work with the binary numbers, how to assign, conversion and bitwise operations on binary numbers?. We then examine how to modify the binomial schemes so as to incorporate the discrete dividend feature, early exercise and call features. Lowest common ancestor in a BST. The ultimate goal of the binomial options pricing model is to compute the price of the option at each node in this tree, eventually computing the value at the root of the tree. A probability tree has two main parts: the branches and the ends. The H2O Python Module. Notes [ edit ] Because Python uses whitespace for structure, do not format long code examples with leading whitespace, instead use. October 26, 2017. Subscribe to the Python Graph Gallery! Enter your email address to subscribe to this blog and receive notifications of new posts by. You divide at random the samples into K parts with a size about the same. (a) Write a Python function that takes n ≥ 1 and returns a n. Ok, first I will try and explain away the problems of the names kD-Tree and kNN. It may not call any helper functions. Similarly in a trinomial tree, each node leads to three other nodes in the next time step. The resulting tree is of rank 3 with 2 3 = 8 nodes. Already have a WordPress. Binomial Distribution in Python. Assuming a two period binomial model and, estimating , we can infer that the stock can move in any of the following ways If the latter were to be true, we could only exercise the option in 1 out of the 3 possible end-states since both 95. The majority of data analysis in Python can be performed with the SciPy module. csv', encoding=. Open Digital Education. Having written about pricing American-style options on a binomial tree in q, I thought it would be instructive to do the same in Python and NumPy. Последние твиты от Green Tree Python man (@tree_python). options python american-options binomial-tree. 5 Poisson Distribution. Since the entire binary heap can be represented by a single list, all the constructor will do is initialize the list and an attribute currentSize to keep track of the current size of the heap. the mean value of the binomial distribution) is. Python is a free and powerful tool that can be used to build a financial calculator and price options, and can also explain many trading strategies and test various hypotheses. The two main feature of. For methods ‘complete’, ‘average’, ‘weighted’ and ‘ward’, an algorithm called nearest-neighbors chain is implemented. Python can connect to database. H2O Documentation¶. She squatted on a tree stump and vomited water. for toss of a coin 0. The binomial distribution is one of the most commonly used distributions in statistics. You can create the following output: a table that contains the default statistics from the analysis and additional statistics, such as the probability of the dependent variable taking the current value. Here is what I've got: def Trinomial(type, S0, K, r, sigma, T, N=2000): import numpy as np t = float(T) / N #fixed lambda lam = np. Done Package python-scipy is not available, but is referred to by another package. The American option at that point is worth $40 –$30. To perform a zero-inflated negative binomial model analysis, you must select an input data source. Summary: two-step binomial tree Theorem Assume that the stock price S0 goes either up or down by a factor u > 1 and d < 1 resp. Algorithm: Enter the height of the tree. Below is the list of most common binomial expressions. There are both conceptual and numerical questions in exams to test this topic. Here, we show that the StochPy solutions are in agreement with the analytical outcomes. level The set of nodes equidistant from the root. Binomial Probability Distribution "pmf" is "Probability Mass Function" Natural Language Toolkit (NLTK) - Highlights (Book by Steven Bird) Book Edition: 2009, 1e Lists and strings do not have exactly the same functionality. When the right tree is pulled up, the left tree becomes its left child. Tree = lambda: defaultdict( Tree ). Binomial Options Pricing Model tree. size - The shape of the returned array. The corresponding Python implementation of tree reduction algorithm would look similarly to this: # Generate terminal nodes of binomial tree level = [] print ('Tree level %i' % n) for i in range (0, n+ 1): # Iterate through nodes # Instrument's price at the node pr = price * d ** i * u ** (n-i) # Option value at the node (depending on side). Algorithm: Enter the height of the tree. Tree models present a high flexibility that comes at a price: on one hand, trees are able to. The spreadsheet also calculate the Greeks (Delta, Gamma and Theta). Decision Tree - Regression: Decision tree builds regression or classification models in the form of a tree structure. The binomial distribution is the basis for the popular binomial test of statistical significance. binom¶ scipy. 2 and n’s from 7 to 50. They constructed a binomial model where the first two moments of the discrete and continuous time return processes match. Decision tree python code sample. One important assumption of Rubinstein’s original implied binomial tree is that all paths that lead to the same ending node have the same risk-neutral probability. What is H2O? Installing H2O-3; Starting H2O and Inspecting the Cluster. Binomial Coefficients. Начать читать. It returns the remainder of dividing the left hand operand by right hand operand. The post on introduction to binomial trees outlined the binomial tree method to price options. I'm not grasping one or more fundamental concepts. For method ‘single’, an optimized algorithm based on minimum spanning tree is implemented. another blog I saw used Sci-Kit learn’s RFE (Recursive Feature Elimination) function to determine what to keep or drop, another training course I saw used Backwards Elimination. 3 sun 4 tree. Below is the list of most common binomial expressions. Use the binomial table to answer the following problems. 3 height in a tree 6. Python - Check if key exists in dictionary. Binary Tree bir Tree yapısıdır. The factory maintains an ArrayList of all the TreeNode objects it creates and allows you to create, fetch, and delete TreeNodes in the binomial lattice. githubusercontent. In this post, we will use QuantLib and the Python extension to illustrate a very simple example. Available Green Tree Pythons. However please note, for the research I want to perform a more accurate theoretical pricing method would of course be a nice plus, but I am mainly looking into a relation between underpricing. There's also a difference in how input should be handled between Python 2 and 3. 3 I/O model 14. No pruning reating one rule that result in der them in this I. Python source files (. and download. Python Quickstart. usr/include/c++/8/ostream:108:7: note: no known conversion for argument 1 from 'std::map::iterator' {aka 'std::_Rb_tree_iterator= 0 and p is in the interval [0,1]. Bacaan lanjut. Python-OptionPrcing-Binomial. denes a Markov chain on {1,. (But it works. Trinomial trees in options pricing In the binomial tree, each node leads to two other nodes in the next time step. 2 heap-ordered binary tree 10. › Get more: Python binary valueShow List Health. One important assumption of Rubinstein’s original implied binomial tree is that all paths that lead to the same ending node have the same risk-neutral probability. Compare the keys of the roots of the trees to be combined, the node becomes the root node of the new tree. postorder A way to traverse a tree, visiting the children of each node before the. In a usual binary tournament we see in sports, each cell is the winner over the two cells it tops, and we can trace the winner down the tree to see all opponents s/he had. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. and download. Each of these probabilities are:. Binary tree. Welcome to my Learning Apache Spark with Python note! In this note, you will learn a wide array of concepts about PySpark in Data Mining, Text Mining, Machine Learning and Deep Learning. binomial function. Finally, the advantages of the model are listed and a simulation is carried out showing that the distribution of prices simulated along the tree is skewed and leptokurtic. Salvatier J. To get to the highest (110) or lowest (90) node of the final step of the tree requires, respectively, four stock up moves or four stock down moves. For that, the needed interfaces should be added to the wrappers. Most people use a binomial distribution table to look up the answer, like the one on this site. The root is the second item in the array. Here is what I've got: def Trinomial(type, S0, K, r, sigma, T, N=2000): import numpy as np t = float(T) / N #fixed lambda lam = np. The binomial tree Bk consists of two binomial trees Bk-1 and they are connected such that the root of one tree is the leftmost child of the other. Assuming a two period binomial model and, estimating , we can infer that the stock can move in any of the following ways If the latter were to be true, we could only exercise the option in 1 out of the 3 possible end-states since both 95. $155 USD in 3 days (0 Reviews). Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. With an edge $$u-v$$$ weight $$w$$$that is not in the MST, take max answer $$w$$$ + Max weighted edge on that path $$u-v$$$on the MST. or precondi- iiven the above te preconditions ichever of these accuracy, then ep. 2 heap-ordered binary tree 10. The implementation of a method is far simpler than the hedging argument. Given three integers, A, X and n, the task is to print terms of below binomial expression series. Writing newick trees. Basic tree attributes. February 11, 2016 Tiago Hands Leave a comment. The Stern-Brocot Tree and Farey Sequences. Growing the tree beyond a certain level of complexity leads to overfitting. There are two modules in Python for YAML: PyYAML and ruamel. Available Green Tree Pythons. (b) Write a Python function that takes n ≥ 2 and returns a n, but throws an Exception for n < 2. Binary Tree Preorder Traversal - LeetCode 144 Python Mp3. denes a Markov chain on {1,. A poisson or binomial regression algorithm seems to do the trick. the payoffs in case of an European Option. 10 Pruning a Decision Tree in Python. A binary tree is a tree in which every node has at most 2 children i. Introduction to Option Pricing with Binomial Trees This section will consider the pricing of a vanilla option using a Binomial Tree. Winslow Murdoch. Similarly in a trinomial tree, each node leads to three other nodes in the next time step. A simple explanation of how to perform a Binomial Test in Python. Binomial trees provide an efficient way to calculate the price of American options. Decision Tree Python Code Sample. Viewed 1k times 0. •The only difference in the binomial tree occurs at the S dd node, where the stock price is$30. Binomial Distribution. import time import zmq. † The two nodes A and C, which bracket node B, are the destinations of the other two branches from node X. We then examine how to modify the binomial schemes so as to incorporate the discrete dividend feature, early exercise and call features. I would now like to visualize the binomial tree such that at each node the. $\begingroup$ The tree method is not exported to Python. 5, the distribution is skewed to the left. Binary Tree Problems -- practice problems in increasing order of difficulty Section 3. Binomial Interest Rate Tree Question. Binary tree. We begin by computing the value at the leaves. the simpler binomial method and move onto the more complex Longstaff-Schwartz method. It includes everything in Python 3. The binomial coefficient uses factorial functions whose values are simplified:. This release adds support for native Python types in templates. In a binomial tree, the underlying asset’s price S, changes in set amounts u>1 and d<1 in each discrete time period. Trying a Python R-tree implementation. size - The shape of the returned array. Thus, it is better to download all the code into a local directory before running. io; binomial coefficient python; binomial theorem in python; biquadratic curve fitting python; bitbucket rest api python example; bitcoin with python; blender change text during animation; blender show python. 20 Comments on R-tree Spatial Indexing with Python. The binomial tree B0 has one node. It's formula to find probability mass function & how one. The following examples illustrate how to perform binomial tests in Python. leaf A bottom-most node in a tree, with no children. com THE WORLD'S LARGEST WEB DEVELOPER SITE. 10 Pruning a Decision Tree in Python. Implementing the binomial tree option pricing model in Python Primary keys, foreign keys, and joins in SQL Project: Binomial tree implementation in Python (17. This algorithm predicts the next word or symbol for Python code. share | improve this question | follow | asked Jan 27 '19 at 14:43. Welcome to my Learning Apache Spark with Python note! In this note, you will learn a wide array of concepts about PySpark in Data Mining, Text Mining, Machine Learning and Deep Learning. Trie (Prefix Tree, 26-ary Tree) Radix Tree (Compact Trie) Ternary Search Tree (Trie with BST of children) B Trees; B+ Trees; Sorting ; Comparison Sorting. 5 week old until after writing it to a brand new SanDisk Micro SD card, the ext4 filesystem gave a bunch of inode er. They constructed a binomial model where the first two moments of the discrete and continuous time return processes match. Decision boundaries created by a decision tree classifier. binom¶ scipy. Posts: 4 Threads: 1 Joined: Nov 2018 Reputation: 0 Likes received: 0. The decision tree classifier is the most popularly used supervised learning algorithm. or precondi- iiven the above te preconditions ichever of these accuracy, then ep. ipynb Visualizing Binomial Trees. For example, the following code describes a 3 stage Bernoulli process where an unfair coin is tossed 3 times (with probability of it giving heads being 0. Lowest common ancestor in a BST. 2 heap-ordered binary tree 10. 1 Lattice tree methods We start this section by revisiting the binomial model and consider its con-tinuous limits. I am a new member on this list. For example, the order 3 binomial tree is connected to an order 2, 1, and 0 (highlighted as blue, green and red respectively) binomial tree. Use the sum() and len. Binary Tree Structure -- a quick introduction to binary trees and the code that operates on them Section 2. , the method for computing the price of American call options and the construction of the early exercise premium in the Black-Scholes-Merton framework from section 18. Bubble Sort ; Selection Sort ; Insertion Sort; Shell Sort ; Merge Sort ; Quck Sort ; Bucket Sort; Counting Sort; Radix Sort; Heap Sort; Heap-like Data Structures ; Heaps; Binomial Queues. We're taking this tree to the k-th dimension. The modulo operation is supported for integers and floating point numbers. Understanding ETE Trees. 'https://raw. Hi i am experience with python 2. Binomial Options Pricing Model tree. Tree = lambda: defaultdict( Tree ). binomial tree and upper triangular matrices were both sound choices. 3 in-order number 6. For method ‘single’, an optimized algorithm based on minimum spanning tree is implemented. Decision Tree Python Code Sample. Write a Python program which iterates the integers from 1 to 50. Plotting these two values over time is known as building a binomial tree. 3 The Binomial Tree Model In the branch model that we looked at in the last section, stock prices are only allowed to do one of two things. \$155 USD in 3 days (0 Reviews). Writing newick trees. Having said that, I think your answer may be misinformed due to those differences. It has three parameters: n - number of trials. The value of the option depends on the underlying stock or bond. 1 Working with DataFrames in Python 2. Yayınlanma: 18 Ağustos 2016 Perşembe 09:32:00. Tutorials on Natural Language Processing, Machine Learning, Data Extraction In this tutorial, you will learn how to use Amazon S3 service via the Python library Boto3. Tree Python. Thus, if the stock price is S ocurrently, then at the next point of time its price will either be uS oor dS. But self-balancing binary search trees (or B-trees, similarly) are just way too Maybe there is truly, honestly a very legitimate reason why Python has excluded a binary search tree implementation from. 5 onward, it's much more convenient to cut in at the Abstract Syntax Tree (AST) This is not a tutorial on editing the parse trees for Python code, but some examples of using the parser. Besides having up and down states, the middle node of the trinomial tree indicates no change in state. This program calculates the price of American-style arithmetic average-rate calls (ARO) based on the CRR binomial tree. how two option pricing models, the binomial tree and Black–Scholes models, can be implemented sion on a tree.


text:
## groups...cancellation laws..

Math help in Abstract Algebra: magmas, monoids, semigroups, groups (Lagrange Theorem, Sylow Theorems, etc ...), rings, fields, modules, isomorphism theorems, algebras, group representations, Lie Algebras, irreducible elements, prime elements, invertible elements, units; Field Theory: separable extensions, normal extensions, Galois extensions, Fundamental Theorem of Galois Theory, minimal polynomials, cyclotomic extensions, group of automorphisms, solvability of equations, solvable groups, splitting fields, algebraic closures, norms and traces on My Math Forum.
Math problems in Group Theory Field Theory Rings and Modules Polynomials

### groups...cancellation laws..

sup[pose a finite set G is closed under ans associative product and that both cancellation laws hold in G...prove that G must be a group...thnx in advance
prashantgolu
Newcomer

Posts: 2
Joined: Mon Aug 02, 2010 11:39 am

### Re: groups...cancellation laws..

What have you tried? Where are you stuck? This is a very good question, it would be a shame to have the entire proof given away.

As a starting point, what rules of a group still need to proven?
Turgul
King of Diamonds

Posts: 192
Joined: Mon Aug 02, 2010 12:13 pm

### Re: groups...cancellation laws..

we need to look for the existence of identity element and then to proove that inverse exists...
prashantgolu
Newcomer

Posts: 2
Joined: Mon Aug 02, 2010 11:39 am

### Re: groups...cancellation laws..

Alright, so we need an identity and we need inverses. First thing is first, we need to know that there is an identity before we go looking for inverses. In the end, we are looking for an element $e \in G$ which has no effect when I multiply it by any element, either on the left or on the right. But perhaps it is easier to take things step by step. For a given element $x \in G$, can we find a left identity? a right identity?

If you would like, a hint: what can we say about the function $f_x:G \rightarrow G$ defined by $f_x(g) = xg$ ?
Turgul
King of Diamonds

Posts: 192
Joined: Mon Aug 02, 2010 12:13 pm


text:
# 1-bit EEPROM with 2N7000 MOSFET

#### popcalent

Joined Mar 17, 2018
47
Hello everybody,

I'm trying to design a 1-bit EEPROM with the ultimate goal of designing a 4x4 bit EEPROM. I need it for a bigger project, and I feel I would be wasting the full potential of a commercial EEPROM if I were to use one. For instance, it doesn't make any sense to use a 28C16 if I'm only using 16 bits. I'm using the 2N7000 MOSFET. These are my designs:

For the debugging purposes, my output is just an LED for now. The switch in design (1) can be connected to positive, to negative, or to nothing. When I switch to nothing, the output keeps the last state (positive or negative). But when I turn off the power, the output is not kept.

Design (2) has a push button that works as a Write Enable, and a switch that connects to positive or negative (unlike the switch in (1)). I added a 2N2222 transistor to drive the Write Enable, and a 1uF capacitor. This keeps the output status even after I turn it off, but only for a period of time. I haven't check, but I'd say it's just a few minutes.

How do I design a memory cell that works as a real EEPROM? That is, it keeps the output status after power down forever. I'm a newbie, so I assume my designs are full of mistakes.

Thank you all!

#### ElectricSpidey

Joined Dec 2, 2017
1,671
You are not going to get there in that direction...perhaps some latching relays?

#### popcalent

Joined Mar 17, 2018
47
You are not going to get there in that direction...perhaps some latching relays?
Thanks for your reply. I think that using 16 latching relays would be too bulky, and too expensive. I was trying to emulate the way real EEPROMS works internally. Apparently, I'm not very good at it!

#### dl324

Joined Mar 30, 2015
12,871
I was trying to emulate the way real EEPROMS works internally.
EEPROMs are much like the EPROMs that preceded them. They store charge on a floating gate and are nonvolatile. To do that with regular MOSFETs, you need to use a battery or super capacitor; like Dallas Semiconductor does for some of their NVRAMs, which are battery backed SRAMs. The simplest would probably be anti-parallel CMOS inverters.

EDIT: Before the corrections start, I'll clarify and say that the storage element is similar. EEPROM used a different program/erase method so they didn't require an external programming voltage.

If you can find them, Xicor X2110 would be good. They're 64x4 SRAMs with each bit backed up by an EEPROM. You use them like an SRAM and store before you power down. The CMOS version will automatically restore EEPROM contents to SRAM on power up. They're in an 18 pin DIP.

I have a number of X2210 and find them useful for small nonvolatile memories.

EDIT: eBay has listings for X2210, but I'd be suspicious of them (being counterfeit) and they're asking $5-20. If you're in the US, I'd sell you some. Last edited: Thread Starter #### popcalent Joined Mar 17, 2018 47 EEPROMs are much like the EPROMs that preceded them. They store charge on a floating gate and are nonvolatile. To do that with regular MOSFETs, you need to use a battery or super capacitor; like Dallas Semiconductor does for some of their NVRAMs, which are battery backed SRAMs. The simplest would probably be anti-parallel CMOS inverters. If you can find them, Xicor X2110 would be good. They're 64x4 SRAMs with each bit backed up by an EEPROM. You use them like an SRAM and store before you power down. The CMOS version will automatically restore EEPROM contents to SRAM on power up. They're in an 18 pin DIP. I have a number of X2210 and find them useful for small nonvolatile memories. EDIT: eBay has listings for X2210, but I'd be suspicious of them (being counterfeit) and they're asking$5-20. If you're in the US, I'd sell you some.
The X2210 look interesting. Unfortunately, I moved from the US a year ago, so I'll have to find them somewhere else. How much should I pay for them?

Another solution is to use a backup coin cell (I need to learn how to do that) and use a 74170 (4x4 RAM). I mean, if I have to use a backup battery anyway, I might as well use the IC that does exactly what I want but is a RAM and not an EEPROM. This is what game cartridges did in the 80s/90s.

#### dl324

Joined Mar 30, 2015
12,871

#### DickCappels

Joined Aug 21, 2008
7,442
The only programmable memory I ever used that stayed programmed "forever" was an ancient (by today's standards) PROM that was programmed by blowing nichrome fuses (I warned you that it was ancient). All of the others, given enough time forgot some their programming.

#### popcalent

Joined Mar 17, 2018
47
Another solution is to use a backup coin cell (I need to learn how to do that) and use a 74170 (4x4 RAM). I mean, if I have to use a backup battery anyway, I might as well use the IC that does exactly what I want but is a RAM and not an EEPROM. This is what game cartridges did in the 80s/90s.
On that note, can I just connect the Vcc and GND of the 74170 to the coin cell, and the rest of the pins to the main circuit?

Edit: I just saw your reply about TTL not retaining memory down to 3V

#### dl324

Joined Mar 30, 2015
12,871
On that note, can I just connect the Vcc and GND of the 74170 to the coin cell, and the rest of the pins to the main circuit?
No. TTL requires 4.75V-5.25V or 4.5V-5.5V; depending on supply tolerance.

If you could use a 3V battery, you'd need to prevent it from being charged while the circuit was powered and for the battery to only provide backup to the memory.

#### Papabravo

Joined Feb 24, 2006
16,165
This kind of thinking is actually a counterproductive waste of time. If you need some small quantity of non-volatile storage, you get the cheapest chip you can find, use what you need and ignore the rest. You just can't do everything they do on chips with discrete parts.

#### crutschow

Joined Mar 14, 2008
27,232
Another solution is to use a backup coin cell (I need to learn how to do that)
Use Schottky diodes to isolate the battery.

You could use the CMOS CD4099 8-bit addressable latch, which draws only leakage current in the static state.
A 3V lithium coin cell should maintain its state essentially for the shelf life of the battery.

Last edited:

#### popcalent

Joined Mar 17, 2018
47
Use Schottky diodes to isolate the battery.

You could use the CMOS CD4099 8-bit addressable latch, which draws only leakage current in the static state.
A 3V lithium coin cell should maintain its state essentially for the shelf life of the battery.
Thanks for your reply. Do I need the Schottky diode if the coin cell is only powering the CD4099 and the main power supply is powering the rest of the circuit? Ie. The main power supply won't power the CD4099.

My understanding is that I need the Schottky to isolate the battery if the battery was powering the whole circuit, and, therefore, conflicting with the main power supply. Perhaps I'm wrong.

#### BobTPH

Joined Jun 5, 2013
3,319
For minimum size and cost, I doubt you could beat a 6-pin PIC.

Bob

#### crutschow

Joined Mar 14, 2008
27,232
Do I need the Schottky diode if the coin cell is only powering the CD4099 and the main power supply is powering the rest of the circuit? Ie. The main power supply won't power the CD4099.
That's okay as long as you account for the difference in voltage between the coin cell and the power to the rest of the circuit.
The input signal voltages can be no higher than the battery voltage unless the input current is limited.
A 10kΩ resistor in series with each input will work for that.

Also the output signal voltage of 3V may be marginal if the rest of the circuit is operated from 5V.
One solution is to use two batteries, for an operating voltage of about 6V for the CD4099.

And the CD4099 can not have an output load when the power is off, otherwise it will drain the battery.

What is the supply voltage to the rest of the circuit?
Can it be varied?

Last edited:

#### popcalent

Joined Mar 17, 2018
47
And the CD4099 can not have an output load when the power is off, otherwise it will drain the battery.
How do I do that?
What is the supply voltage to the rest of the circuit?
Can it be varied?
It's 5V, I think I'll do two coin cells for 6V and use a diode to make it 5.3V.

#### popcalent

Joined Mar 17, 2018
47
And the CD4099 can not have an output load when the power is off, otherwise it will drain the battery.
How do I do that? Can I use transistors with their bases connected to the main supply to disconnect each output from GND when the power is off?
What is the supply voltage to the rest of the circuit?
Can it be varied?
It's 5V, I think I'll do two coin cells for 6V and use a diode to make it 5.3V.

#### atferrari

Joined Jan 6, 2004
4,330
Your switches would require debouncing.

#### dl324

Joined Mar 30, 2015
12,871
53 cents, 6-pin SOT23 (same size as many SMT transistors, 128 bytes of Flash data memory.
And if you can’t think of 3 other components it could replace in your design, you haven’t much imagination.
How much glue logic do you think it would take to convert addresses and data from parallel to serial and back? Seriously...

Last edited:


text:
# A question on the Faulhaber's formula

Proposition 1.1 For every integers $$m,n\geq 0$$ the following identity holds $$$$n^{2m+1}=\sum_{k=1}^{n}\sum_{j=0}^m A_{m,j}k\strut^j(n-k)\strut^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(n, k)\cdot n\strut^k,$$$$ where $$U_m(n, k), \ A_{m,j}$$ are coefficients defined as follows

Definition 1.2 (Definition of $$A_{m,j}$$ coefficients.) $$\begin{equation*} A_{m,j}:= \begin{cases} 0, & \mathrm{if } \ j<0 \ \mathrm{or } \ j>m, \\ (2j+1)\binom{2j}{j} \sum_{d=2j+1}^{m} A_{m,d} \binom{d}{2j+1} \frac{(-1)\strut^{d-1}}{d-j} B_{2d-2j}, & \mathrm{if } \ 0 \leq j < m, \\ (2j+1)\binom{2j}{j}, & \mathrm{if } \ j=m. \\ \end{cases} \end{equation*}$$

Definition 1.3 (Definition of $$U_m(\ell, k)$$ coefficients.) $$\begin{equation*} U_m(\ell, k) := (-1)\strut^m \sum_{k=1}^{\ell}\sum_{j=t}^m (-1)\strut^j\binom{j}{t}A_{m,j}k\strut^{2j-t}. \end{equation*}$$

The sense of problem: Entire problem is to prove that Proposition (1.1) directly follows from Faulhaber's formula.

Below we provide our try to solve this problem. Consider the Faulhaber's formula Knuth, page 9: $$$$\label{knuth1} (2.1) \quad \quad n^{2m-1}=\begin{cases} n^1 = \binom{n}{1}, \ &\mathrm{if} \ m=1;\\ n^3 = 6\binom{n+1}{3}+\binom{n}{1}, \ &\mathrm{if} \ m=2;\\ n^5 = 120\binom{n+2}{5}+30\binom{n+1}{3}+\binom{n}{1}, \ &\mathrm{if} \ m=3;\\ \vdots\\ n^{2m-1} = \sum\limits_{1\leq k\leq m}(2k-1)!T(2m,2k)\binom{n+k-1}{2k-1}, \ &\mathrm{if} \ m\in\mathbb{N}; \end{cases}$$$$ The coefficients $$(2k-1)!T(2m,2k)$$ in the Faulhaber's identities (2.1) can be calculated using following formula $$$$(2.2) \quad \quad (2k-1)!T(2n,2k)=\frac{1}{r}\sum_{j=0}^{r}(-1)^j\binom{2r}{j}(r-j)^{2n},$$$$ where $$r=n-k+1$$ and $$T(2n,2k)$$ is central factorial number, see A303675. Consider the partial case of (2.1) for $$m=2$$, for instance $$$$(2.3) \quad \quad n^3=\sum_{k=1}^{n} 6\binom{k}{2}+1=\sum_{k=1}^{n}6k(n-k)+1$$$$ The l.h.s of identity (2.3) is reached by means of Hockey Stick pattern in terms of Binomial coefficients $$$$\sum_{k=s}^{n}\binom{k}{s}=\binom{n+1}{s+1}$$$$ It follows from the identity (2.3) that $$$$\sum_{k=1}^{n}\binom{k}{2}=\sum_{k=1}^{n}k(n-k)$$$$ Now, lets keep our attention to the identity (2.3) again. As we said, this is the partial case of Faulhaber's formula for $$m=2$$, and we can notice that the following structure of (2.3) can be assumed $$\begin{equation*} n^{3}=\sum_{k=1}^{n}\sum_{j=0}^{m=1} A_{m,j}k\strut^j(n-k)\strut^j \end{equation*}$$ and, consequently, for each non-negative integer $$m$$ $$\begin{equation*} (2.4)\quad \quad n^{2m+1}=\sum_{k=1}^{n}\sum_{j=0}^{m} A_{m,j}k\strut^j(n-k)\strut^j \end{equation*}$$ The coefficients $$A_{m,j}$$ in (2.4) are terms of sequences: A302971 - numerators; A304042 - denominators. More info concerning the identity $$n^{2m+1}=\sum_{k=1}^{n}\sum_{j=0}^{m} A_{m,j}k\strut^j(n-k)\strut^j$$ can be found at this link.

Now we get a structure, which seems to be direct consequence of the Faulhaber's formula, with only one difference, the corresponding binomial coefficients are replaced by the polynomials $$k^j(n-k)^j$$. So, for the moment, the task is to represent the binomial coefficients in terms of polynomial $$k^j(n-k)^j$$. Let's introduce the function $$$$(2.5)\quad \quad F_s(n,k)=k\binom{n-k}{s-1}=k\sum_{j=0}^{n-k-1}\binom{j}{s-2}$$$$ For instance, $$$$\begin{split} s=1: \ F_1(n,k) &=0\\ s=2: \ F_2(n,k) &=k(n-k) \\ s=3: \ F_3(n,k) &=k(n-k)(n-k-1)/2\\ s=4: \ F_4(n,k) &=k(n-k)(n-k-1)(n-k-2)/6 \end{split}$$$$ And most importantly $$$$(\star)\quad \quad \sum_{k=0}^{n}\binom{k}{s}=\sum_{k=0}^{n}F_s(n,k)$$$$ As we already have the run-algorithm for $$m=2$$ in Faulhaber's formula that is $$n^3$$, lets take another example, for $$m=3$$ and corresponding result $$n^5$$, we will apply recently received results (1.6) and (1.7). By Faulhaber's formula, the fifth power is $$$$(2.6)\quad \quad n^5 = 120\tbinom{n+2}{5}+30\tbinom{n+1}{3}+\tbinom{n}{1}$$$$ Our main aim is to compile expression (2.6) to the form $$n^{5}=\sum_{k=1}^{n}\sum_{j=0}^{2} A_{2,j}k\strut^j(n-k)\strut^j$$. By the identity $$(\star)$$ and definition (2.5) we have $$$$\begin{split} &\sum_{k=1}^{n}\tbinom{k+1}{4}=\sum_{r=1}^{n}F_4(n,k+1)=\sum_{r=1}^{n}-(1/6) k (-1 + k - n) (k - n) (1 + k - n)\\ &=1/6(kn^3-3k^2n^2+3k^3n-k^4-kn+k^2) \\ &\sum_{k=1}^{n}\tbinom{k}{2}=\sum_{k=1}^{n}F_2(n,k)=\sum_{k=1}^{n}k(n-k)\\ &\sum_{k=1}^{n}\tbinom{k-1}{0}=\tbinom{n}{1}=n \end{split}$$$$ Let be $$a=n-k$$ in $$F_4(n,k)=1/6k(n-k)(n-k+1)(n-k-1)$$, thus $$$$\begin{split} F_4(n,k) &=1/6k(a^3-a)\\ &=1/6k((n-k)^3-(n-k))\\ &=1/6k[n^3-3kn^2+3k^2n-k^3-n+k]\\ &=1/6(kn^3-3k^2n^2+3k^3n-k^4-kn+k^2) \end{split}$$$$ Let's substitute $$F_2(n,k)$$, and $$F_4(n,k)$$ to the equation (2.6), respectively $$$$\begin{split} n^5 &= 120\sum_{k=1}^{n}1/6(kn^3-3k^2n^2+3k^3n-k^4-kn+k^2)+30\sum_{k=1}^{n}kn-k^2+\sum_{k=1}^{n}1\\ &= 20\sum_{k=1}^{n}(kn^3-3k^2n^2+3k^3n-k^4-kn+k^2)+30\sum_{k=1}^{n}kn-k^2+\sum_{k=1}^{n}1\\ &= 20\sum_{k=1}^{n}(kn^3-3k^2n^2+3k^3n-k^4)-20\sum_{k=1}^{n}kn+k^2+30\sum_{k=1}^{n}kn-k^2+\sum_{k=1}^{n}1\\ &= 20\sum_{k=1}^{n}k(n-k)^3+10\sum_{k=1}^{n}k(n-k)+\sum_{k=1}^{n}1\\ &= \sum_{k=1}^{n}20k(n-k)^3+10k(n-k)+1 \end{split}$$$$ As we can see, the form of the our transformation is different from $$n^{5}=\sum_{k=1}^{n}\sum_{j=0}^{2} A_{2,j}k\strut^j(n-k)\strut^j$$, but still is near to the result $$n^{5}=\sum_{k=1}^{n}30k^2(n-k)^2+1$$. We can see that if the variable of polynomial at $$n^5=\sum_{k=1}^{n}20k(n-k)^3+10k(n-k)+1$$ would be $$k^2(n-k)^2$$ then we get desired result $$n^{5}=\sum_{k=1}^{n}30k^2(n-k)^2+1$$.

The problem: Revise the function $$F_s(n,k)$$ such way, that the construction $$n^{5}=\sum_{k=1}^{n}\sum_{j=0}^{m} A_{m,j}k\strut^j(n-k)\strut^j$$ directly follows when corresponding binomial coefficient sums in Faulhaber's formula (2.1) is replaced by sums of $$F_s(n,k)$$.

PS For those who interested, we collected a few questions concenring, everybody are invited to participate, visit https://kolosovpetro.github.io/math_project/

• Is it possible to precisely formulate the open question, i.e. what the statement to prove is? (At the moment it seems somehow crowded with additional information; it is good in general to have it, but makes it hard to extract the actual question.) – Daniel Krenn Feb 4 at 13:31
• Thank you for your comment, see the PDF with more clear stated question, now i will revise this one as well – Petro Kolosov Feb 4 at 16:21