scholarly journals Approximate Model Checking Using a Subset of First-order Logic

2010 ◽  
Vol 3 ◽  
pp. 268-282 ◽  
Author(s):  
Kiyoharu Hamaguchi ◽  
Kazuya Masuda ◽  
Toshinobu Kashiwabara
Keyword(s):  
Model Checking ◽  
Approximate Model ◽  
Order Logic ◽  
First Order Logic ◽  
First Order

scholarly journals “Most of” leads to undecidability: Failure of adding frequencies to LTL

2021 ◽  
pp. 82-101
Author(s):  
Bartosz Bednarczyk ◽  
Jakub Michaliszyn
Keyword(s):  
Model Checking ◽  
Formal Verification ◽  
Temporal Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Statistical Reasoning ◽  
First Order ◽  
High Interest ◽  
The Past ◽  
Influence Networks

AbstractLinear Temporal Logic (LTL) interpreted on finite traces is a robust specification framework popular in formal verification. However, despite the high interest in the logic in recent years, the topic of their quantitative extensions is not yet fully explored. The main goal of this work is to study the effect of adding weak forms of percentage constraints (e.g. that most of the positions in the past satisfy a given condition, or that $$\sigma $$ σ is the most-frequent letter occurring in the past) to fragments of LTL. Such extensions could potentially be used for the verification of influence networks or statistical reasoning. Unfortunately, as we prove in the paper, it turns out that percentage extensions of even tiny fragments of LTL have undecidable satisfiability and model-checking problems. Our undecidability proofs not only sharpen most of the undecidability results on logics with arithmetics interpreted on words known from the literature, but also are fairly simple. We also show that the undecidability can be avoided by restricting the allowed usage of the negation, and discuss how the undecidability results transfer to first-order logic on words.

AUTOMATED TERMINATION IN MODEL-CHECKING MODULO THEORIES

2013 ◽  
Vol 24 (02) ◽  
pp. 211-232 ◽  
Author(s):  
ALESSANDRO CARIONI ◽  
SILVIO GHILARDI ◽  
SILVIO RANISE
Keyword(s):  
Model Checking ◽  
Sufficient Conditions ◽  
Order Logic ◽  
Satisfiability Modulo Theories ◽  
First Order Logic ◽  
Reachability Problem ◽  
First Order ◽  
Recent Advances ◽  
Infinite State Systems ◽  
Infinite State

We identify sufficient conditions to automatically establish the termination of a backward reachability procedure for infinite state systems by using well-quasi-orderings. Besides showing that backward reachability succeeds on many instances of problems covered by general termination results, we argue that it could predict termination also on interesting instances of the reachability problem that are outside the scope of applicability of such general results. We work in the declarative framework of Model Checking Modulo Theories that permits us to exploit recent advances in Satisfiability Modulo Theories solving and model-theoretic notions of first-order logic.

scholarly journals Satisfiability in Strategy Logic Can Be Easier than Model Checking

2019 ◽  
Vol 33 ◽  
pp. 2638-2645 ◽  
Author(s):  
Erman Acar ◽  
Massimo Benerecetti ◽  
Fabio Mogavero
Keyword(s):  
Model Checking ◽  
Order Logic ◽  
First Order Logic ◽  
Multi Agent Systems ◽  
First Order ◽  
Systems Model ◽  
Multi Agent ◽  
Decidable Fragment ◽  
Game Theoretic ◽  
Strategy Logic

In the design of complex systems, model-checking and satisfiability arise as two prominent decision problems. While model-checking requires the designed system to be provided in advance, satisfiability allows to check if such a system even exists. With very few exceptions, the second problem turns out to be harder than the first one from a complexity-theoretic standpoint. In this paper, we investigate the connection between the two problems for a non-trivial fragment of Strategy Logic (SL, for short). SL extends LTL with first-order quantifications over strategies, thus allowing to explicitly reason about the strategic abilities of agents in a multi-agent system. Satisfiability for the full logic is known to be highly undecidable, while model-checking is non-elementary.The SL fragment we consider is obtained by preventing strategic quantifications within the scope of temporal operators. The resulting logic is quite powerful, still allowing to express important game-theoretic properties of multi-agent systems, such as existence of Nash and immune equilibria, as well as to formalize the rational synthesis problem. We show that satisfiability for such a fragment is PSPACE-COMPLETE, while its model-checking complexity is 2EXPTIME-HARD. The result is obtained by means of an elegant encoding of the problem into the satisfiability of conjunctive-binding first-order logic, a recently discovered decidable fragment of first-order logic.

scholarly journals EPR-based k-induction with Counterexample Guided Abstraction Refinement

10.29007/scv7 ◽  
2018 ◽  
Author(s):  
Zurab Khasidashvili ◽  
Konstantin Korovin ◽  
Dmitry Tsarkov
Keyword(s):  
Model Checking ◽  
Bounded Model Checking ◽  
Order Logic ◽  
Experimental Results ◽  
Theorem Prover ◽  
First Order Logic ◽  
Safety Properties ◽  
Abstraction Refinement ◽  
First Order ◽  
Automated Theorem Prover

In recent years it was proposed to encode bounded model checking (BMC) into the effectively propositional fragment of first-order logic (EPR). The EPR fragment can provide for a succinct representation of the problem and facilitate reasoning at a higher level.In this paper we present an extension of the EPR-based bounded model checkingwith k-induction which can be used to prove safety properties of systems overunbounded runs. We present a novel abstraction-refinement approach based onunsatisfiable cores and models (UCM) for BMC and k-induction in the EPR setting.We have implemented UCM refinements for EPR-based BMC and k-induction in a first-order automated theorem prover iProver. We also extended iProver with the AIGER format and evaluated it over the HWMCC'14 competition benchmarks. The experimental results are encouraging. We show that a number of AIG problems can be verified until deeper bounds with the EPR-based model checking.

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