Questions tagged [model-checking]
Model checking refers to the following problem: given a model of a system, test automatically whether this model meets a given specification.
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Is model checking PSpace-hard *in formula size*?
Sistla/Clarke proved [SC82] that the LTL model-checking problem is PSpace-complete.
Sometimes people write that this problem is "PSpace-hard in $|\phi|$" (e.g. [LP85]). What does this mean formally?
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4
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Are two CCS processes equivalent with respect to weak bisimilarity if and only if they satisfy exactly the same set of HML formulas?
I was skimming this recent paper and I was struck by the following statement:
two processes are equivalent with respect to weak bisimilarity if and only if they satisfy exactly the same set of HML ...
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1answer
95 views
Negation of the semantics of the Until operator in LTL
I have been looking at the Until operator and the release operator and when introduced to the release operator it was suggested that it is equivalent to:
$\phi R \psi \equiv \neg(\neg\phi U \neg \psi)...
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(Generally) How to specify asynchronous action with side effects using logic equations
Say you have this function call sequence:
function all() {
fn1()
fn2()
fn3()
}
And say that fn2 was asynchronous and ...
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2answers
97 views
Buchi automata in formal software verification
As I am studying the application of Buchi automata in formal software verification, I am interested in the computational complexity (or links to papers) for the algorithms used to solve the problem in ...
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1answer
44 views
Model Checking CTL* algorithm
Currently I'm trying to understand the CTL* model checking algorithm from this book. The basic idea is clear to that we can use the LTL algorithm to whenever we have a subformular $E\phi$ or $A\phi$ ...
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1answer
50 views
Validity of CTL formula $s_0 \models EG\ AF\ p$ in given model
I have been learning Verification by model checking recently and I get the following question:
Is the CTL formula $s_{0} \models EG\ AF\ p$ valid in the following model?
I think it is ...
2
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1answer
46 views
How to prove a LTL formula correct in a specific model?
I have been learning Verification by model checking recently and I get the following question:
$Whether\ the\ LTL\ formula\ M, q_3\ \models (X\ \lnot a) \rightarrow (F\ G\ \lnot a)\ is\ established\ ...
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12 views
Timed Kripke structures with inequality constraints
I am having problems creating a timed Kripke structure $\mathcal{TK} = \langle S, \mathcal{T}, \rightarrow, L \rangle$ for a system that I have.
My system, a timed automaton system (time base $\...
2
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1answer
58 views
How do you correctly write this sentence as a CTL formula?
Sentence: From every reachable state it is possible to reach a state where $p$ is true.
How do you write this sentence as a CTL formula? So far I only dealt with CTL syntax and trees but maybe it ...
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2answers
81 views
How to express the existence of winning strategy of the starter of a game in temporal logic?
Consider a two-player game. A winning strategy of a player is a strategy following which the player can always beat his opponent, no matter how his opponent responds.
A game can be unfolded to a ...
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41 views
How to collect all states of a behavior in TLA+?
Description of the problem:
I am modeling checking a distributed protocol against a global property with TLA+ developed by Leslie Lamport. The global property is defined on all states of a behavior (...
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How Model Checking works with User Interaction
In order to understand how to apply Model Checking, I am wondering how to apply it to a pseudo-realistic async program.
Say I have the following pseudocode:
...
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1answer
122 views
How to define the Atomic Propositions in Model Checking
The atomic propositions in Symbolic Model Checking form the state in the state-transition graph (the model $\mathcal{M}$ in Model Checking). The other part of Model Checking is the specification, ...
2
votes
1answer
60 views
What exactly state is in Model Checking
So I finally realized the difference between transition systems and automata, and now am closer to understanding Model Checking. One of the last pieces is understanding what exactly "state" is in ...
2
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1answer
155 views
Least fix point of CTL formula
In the book Logic in Computer Science on page 244, there is a proof that $[[E(\phi U\psi)]]$ is the least fixed point of $G(X)=[[\psi]] \cup ([[\phi]]\cap\mathop{\textrm{pre}}_\exists(X))$. I don't ...
4
votes
1answer
216 views
How does TLC check liveness properties?
The paper "Model Checking TLA+ Specifications" published in 1999 explained how TLC (Temporal Logic Checker) checks safety properties written in TLA+ developed by Lamport. At that time, TLC did not yet ...
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CTL satisfied by Kripke Structure
given a Kripke Structure I want to check if a CTL formula is satisfied or not.
the CTL is: $$ AG(c \vee AX\neg E((a\vee b)Uc)) $$
I have read that it is better to write to CTL in terms of $\wedge $ ...
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37 views
How to Construct Kripke Structure States from Nested Functions
Say I have these defined functions:
...
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53 views
Understanding a Single Step in the Model Checking Algorithm
This answer explains roughly how to convert a nested boolean function into a Binary Decision Diagram (BDD). This question is about how to structure the states for the BDD. Now in this question I am ...
2
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0answers
146 views
Equivalence preserving operator from CTL* to LTL
The question is about an operator that transforms any CTL* formula ${\psi}$ into a (not necessarily equivalent) LTL formula ${A\psi^d}$, where $d$ means syntactically removing all $A,E$ quantifiers ...
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2answers
50 views
How to prove a side effect in a function
I asked a question earlier about Saving to the Database, which was very general and about the requirements for a proof when you go through many layers of non-verified systems such as the network and ...
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1answer
43 views
What the State is, and Where it comes from, when Generating Reachability Graphs
For Timed Automata, I found Figure 1 below. For Coloured Petri Nets I found Figure 2. Both are for "Reachability Graph Construction".
However, they don't describe where they got the states from (...
2
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1answer
55 views
Acceptance conditions when translating LTL to Büchi automaton?
As an exercise in better understanding, I have been implementing the LTL to Generalized Büchi Automaton translation algorithm of Gerth, et al. (which is also discussed in Clarke, et al., Model ...
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Why do we have free variables in mu-calculus?
I'm reading the Model Chekcing book of E. M. Clarke and in the chapter about µ-calculus there is an example formula
$$
f = \mu Z. ((q \mathrel{\mathrm{AND}} Y) \mathrel{\mathrm{OR}} \langle a \rangle ...
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1answer
217 views
Explanation of the Gelfond Lifschitz reduct
Can someone explain with a hands on example how the Gelfond Lifschitz reduct works in order to check stable model semantics?
edit
a simple example here - at least as far as I understand the thing. ...
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1answer
64 views
Given two formulae E[G F p] (which is CTL*) and EG EF p ( which is a CTL) with a Model prove that they are not equivalent
I am trying to prove they are not equivalent , a model which satisfies the fist one but not the second since I think EG EF p is stronger than E[GF p],any leads would be helpful. Thanks.
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1answer
35 views
Finding Models for a sequent
I am trying to generate models for the following sequent.
$$\exists x \exists y \forall z (z = x \lor z = y)$$
What I have come up with is this.
$$A= \{0,1\}$$
So in this model, for all the values ...
0
votes
1answer
97 views
LTL to GBA versus LTL to BA
Let's assume that I have an LTL formula and I want to convert it to a Buchi automaton. For which fragment of LTL, GBA is more succinct and for which fragment BA has the same size as GBA.
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73 views
Importance of Needham–Schroeder Protocol
I'm working on a paper about model checking on cryptographic protocols and many of the papers I have read, base their approaches in the Needham-Schroeder protocol. I undestand this was one of the ...
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0answers
89 views
Calculate expected values of “Craps Game” with the help of Prism Model Checker
I have modelled the craps game (https://en.wikipedia.org/wiki/Craps#Rules_of_play) as a dtmc with the prism model checker:
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1answer
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CTL* query evaluation order
I'm currently trying to evaluate a CTL* expression and am not sure how to stepwisely evaluate the queries.
For example I have EFG p. This means something like 'there is a path where eventually there ...
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How the $EX(f)$ is evaluated in symbolic model checking?
I was reading the symbolic model checking, So there it has mentioned that we can represent the set of states and transition relations of any transition system with the help of ROBDDs.
I was trying to ...
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votes
1answer
147 views
Programming language semantics prototyping tool
Is there any tool for prototyping a programming language semantics and type system and that also allows for some sort of model checking of standard properties, like type soundness?
I'm asking this, ...
2
votes
1answer
232 views
Modeling a sequential circuit as a transition system
I was asked to model the following sequential circuits C1, C2 as transition systems (i.e. identify the output y function and register functions r1, r2, r3)
For C2 there appears to be not input x and ...
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102 views
generic technique to build LTL/CTL formula that satisfy specific inputs to a model
I have an automaton, for example the below automaton and would like to generate a single formula (LTL or CTL, or some other representation) that satisfy exactly the traces provided. e.g.,
$t_1 = i^*...
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1answer
157 views
How to verify a property about a certain order of events in TCTL / UPPAAL?
I'd like to check if a certain order of events happens if another property holds true using UPPAAL and TCTL.
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1answer
85 views
Can QBF encode #QBF?
In another question Initializing non-deterministic variables in QBF, I was interested about translating assertion-based pseudocode to QBF in order to have an exponentially more compact encoding ...
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1answer
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Initializing non-deterministic variables in QBF
I'm trying to translate the following pseudocode to QBF. The integers are encoded as simple fixed-width bitvectors, and the entire procedure runs in polynomial space ensuring QBF has enough ...
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1answer
135 views
What's the definition of ACTL?
I have been looking for the definition of ACTL, but Google has given me very little to go with.
So far, I know ACTL is another form of CTL model checking, and CTL includes the following operators:
...
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1answer
391 views
How to prove LTL-formulas true for all paths?
I'm quoting a question from my homework which I don't understand its wording.
Also, I'm not looking for an answer for my problem, I just want to be pointed at some articles/tutorials/reading/tips to ...
5
votes
1answer
137 views
The importance of the language semantics for code generation and frameworks for code generation in model-driven development
I am implementing worflow where the code in industrial programming languages (JavaScript and Java) should be generated from the formal (formally verified) expressions (from ontologies as objects and ...
2
votes
1answer
347 views
LTL properties in bounded model checking via assertions
Is there a way to check LTL properties in a bounded model checker?
As an example, consider a liveness property ($G F p$ - always eventually $p$)? Suppose we have the following trivial program
...
2
votes
1answer
437 views
The Interleaved Transition System for 2 Independent and Concurrent Transition Systems
This question is about Model Checking for Software Formal Verification
How do you model the joint behavior of 2 independent and concurrent transition systems?
Specifically, given the two independent ...
2
votes
1answer
206 views
What's a side-effect free expression in Timed Automata?
I'm trying to get myself more familiar with Timed Automata theory. At some point I came across the expression "side-effect free" like in the following:
A guard is a side-effect free expression that ...
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2answers
703 views
What does least fix point and greatest fix point mean in Safety games
In safety games there are these mathematical notation about greatest fix points and least fix points but I don't get it. How would we describe them plain English without mathematical symbols.
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Determining which states in a transition system satisfy a specific CTL formula [closed]
Trying to answer the following question:
However, my answer is that only one of these states satisfy the TS (which is for sure wrong since the next part of this question asks to remove states that ...
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vote
1answer
150 views
Find equivalent LTL formula, without Y (Yesterday) operator. How can I handle first state?
The task is to find an equivalent LTL formula for $G(a \Rightarrow Yb)$, which doesn't contain the Y operator. My idea is to search for invalid path patterns with 2 $a$'s in a row, e.g. bbbbaab.
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1answer
107 views
An algorithm to compute a set of states that satisfy a specific CTL formula
Working through a past exam question and I'm unsure where to start or what form they want the answer in:
Define an algorithm that receives as input a finite transition
system TS defined over the set ...
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1answer
273 views
Given a set of LTL formulas, on which states does the Kripke structure hold? [closed]
I'm currently learning about LTL and CTL formulas and to get a better understanding I try to manually interpret the formulas over a given Kripke structure. Since I'm not 100% sure if my results are ...
