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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Are automata useful in software verification?

I contrast the paradigm of SMT-based verification of software, such as in LiquidHaskell with the approach based on automata. To me it appears that automata are only used in the paradigm of model ...
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Algorithm for computing $Pr[s \vDash C \bigcup^{\geq n} B]$ for probabilistic verification

I'm having some difficulty trying to come up with an algorithm for computing $Pr[s \vDash C ~\bigcup^{\geq n} B]$ given a finite Markov chain where $S$ is the set of states, $s \in S$, $B,C \subseteq ...
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Does the reduction of places and transitions in Petri nets bring any benefits for model checking?

I have a process model P and I have transformed it with some rules to Petri net p1 and with some different rules to Petri net <...
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$Sat(EG^2\alpha)$ as a fixpoint of an operator

Currently I am studying CTL model checking. I found this exercise: Consider the CTL formula $EG^2(\alpha)$ which means that there exists a path that satisfies $\alpha$ at every even position. Define $...
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Is there a tool that can check whether m |= p holds, where m and p are both ltl formula

To the best of my understanding, m |= p asks whether the ltl formula p satisfies the ltl formula m. In other words, m -> p is a tautology. Here are some example of where m |= p hold: ...
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Does Rice's theorem apply to sequential logic circuits?

I am wondering if Rice's theorem (or something similar to that) applies also to sequential circuits. I.e. given any finite sequential circuit, can there be an algorithm that can formally verify any ...
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Check if given safety properties are regular, and if so construct NFAs

Let $\mathit{AP} = \{a, b, c\}$. Consider the following LT properties: Between two neighboring occurrences of $a$, $b$ always holds. Between two neighboring occurrences of $a$, $b$ occurs more often ...
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Satisfaction of CTL

I'm trying to compute Sat(Φ), but I can't seem to figure out this question, what i understood is that I first need to solve Sat(req U -busy), but it doesn't make sense, how can it be that req is true ...
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Transition System Problem

I'm very confused about this question, would it be correct to say that (a) is false since executing the state ~req ready being repeated would invalidate that statement ?
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Definition of liveness property in model checking

A property $P$ is simply a set of sequences of states and a certain program is characterized by its set of sequences of states, let's call it $T$. A program is compliant to a specific property P if $T\...
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Automaton-based model checking on finite traces

I want to check whether a formula in finite LTL is valid on a finite, linear trace. For infite traces I would create a Kripke structure of the trace and a Büchi automaton for the negated formula, ...
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Fault localisation using model checking

In many papers like Empirical Evaluation of the Tarantula Automatic Fault-Localization Technique there is a good explanation about how tarantula algorithm can be used with test suits. Is there any ...
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What are the limitations of symbolic model checking?

What are the limitations of the Symbolic Model Checking? As far as I know, "state-space explosion" can still happen by this technique but it can explore much larger state space. So, is the Symbolic ...
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What goes into proving two complicated programs are equivalent?

Say I wanted to prove that two programs were equivalent (either rigorously if possible, or informally if not). More specifically, say I have something relatively complex such as an HTTP server ...
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Review of Formal Verification and How to Apply it to Greenfield Project [duplicate]

Last year I looked heavily into Formal Verification, such as automated theorem proving, model checking, type systems, symbolic evaluation, and many others. I probably spent a few weeks or maybe months ...
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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 ...
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Proving that a property is k-inductive with an SMT solver (parametric resettable counter)

I'm following the slides at https://homepage.cs.uiowa.edu/~tinelli/talks/FT-11.pdf where Tinelli explains how k-induction works in the context of SMT based model checking. A parametric and resettable ...
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Modeling a set of probabilistic concurrent processes

I'm looking into discrete-time Markov chains (DTMCs) for use in analyzing a probabilistic consensus protocol. One basic thing I haven't been able to figure out is how to model a set of independent ...
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Safety property vs Liveness property

If i take a safety property $SP$ and a liveness property $LP$, is it true that the result of their intersection is a safety property (and not a liveness property) ? Why ? Thanks
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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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Calculating probability of reaching state in DTMC

Consider a highly-connected graph of states & transitions where each transition is marked with a weight (representing probability of occurring) and the graph satisfies the Discrete Time Markov ...
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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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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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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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(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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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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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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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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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 ...
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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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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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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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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 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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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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What exactly is Symbolic Model Checking?

I know that Symbolic Model Checking is state space traversal based on representations of states sets and transition relations as formulas like in CTL using models like Kripke Model. I know the theory. ...
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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, ...
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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 ...
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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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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 ...
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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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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 (...
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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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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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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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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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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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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 ...
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What is the difference between a Transition System and a Program Graph? (model checking) [closed]

As the above question says. I'm wondering if a transition system is the same as a program graph or they are two different things? Thank you.