Logiques temporelles basées sur actions pour la vérification des systèmes asynchrones

Mateescu, Radu

doi:10.3166/tsi.22.461-495

Cited by 5 publications

(3 citation statements)

References 35 publications

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“…Parameterised Boolean Equation Systems (PBES, also known as first-order, or predicate BES) arise as FES over the powerset lattice (2 D , ⊆), with D some data type, typically representing the state space of a possibly infinite LTS. In [Mat98,GM99], PBES are proposed to encode the model-checking problem of first-order mu-calculus on infinite LTSs; they are studied in more detail in [GW05b,GW05a]. An encoding of (branching) bisimulation of infinite LTSs in PBES is proposed in [CPvdPW07].…”

Section: Introductionmentioning

confidence: 99%

Partial-Order Reduction for Parity Games with an Application on Parameterised Boolean Equation Systems

Neele¹,

Willemse²

2021

Preprint

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We study operations on fixpoint equation systems (FES) over arbitrary complete lattices. We investigate under which conditions these operations, such as substituting variables by their definition, and swapping the ordering of equations, preserve the solution of a FES. We provide rigorous, computer-checked proofs. Along the way, we list a number of known and new identities and inequalities on extremal fixpoints in complete lattices.Well-known instances of FES. Boolean Equation Systems (BES) arise as FES over the complete lattice ⊥ < ⊤, and were proposed in [And94, AV95] for solving the model checking and equivalence checking problems on finite labeled transition systems (LTS). BES received extensive study in [Mad97, MS03, GK04, Mat06].An equivalent notion to BES is two-player parity games [EJ91], see [Mad97] for a proof. Algorithms for solving parity games receive a lot of attention, since this is one of the few problems which is in NP and in co-NP, but not known to be in P. Recently, it has been shown that parity games (and thus BES) can be solved in quasi-polynomial time [CJK + 17]. This result has also been lifted to the general setting of FES on finite lattices [HS21, JMT22]. Other types of games can also be seen as an instance of FES, for example energy parity

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Section: Introductionmentioning

confidence: 99%

Partial-Order Reduction for Parity Games with an Application on Parameterised Boolean Equation Systems

Neele¹,

Willemse²

2021

Preprint

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“…This should not cause major technical issues, as fixpoint characterizations for such operators are well-known (see e.g. [6]), but the precise formalization and implementation need to be worked out. -Fairness needs to be reconsidered.…”

Section: Discussionmentioning

confidence: 99%

“…The full syntax and semantics of A-CTL, defined over LTS, can be found in [5]. [6] provides a comprehensive survey of temporal logics with actions, and A-CTL in particular, including fixpoint characterizations of A-CTL operators.…”

Section: Action-based Logicsmentioning

confidence: 99%

Symbolic Model Checking of Logics with Actions

Pecheur

Raimondi

Model Checking and Artificial Intelligence

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Abstract. Reasoning about agents and modalities such as knowledge and belief leads to models where different relations over states co-exist, or equivalently, where information (labels, actions) is associated to state transitions. This paper discusses how to augment classical CTL symbolic model-checking to support logics with actions such as A-CTL (action-CTL), and how this can be implemented using BDDs in tools such as the SMV/NuSMV package. Considering general action-state structures, we first propose a natural extension of CTL to actions, called ActionRestricted CTL (ARCTL) and adapt classical results from CTL to express model checking based on three functions eax, eau and eag. On these grounds, we present two different implementations of symbolic model checking with actions. The first approach encodes action-state models and logics into pure state-based models and logics, that can be checked with existing model-checkers. The second approach consists in a native implementation of the three extended operators. We report on our prototype implementation of both approaches based on NuSMV and give an overview of how this is used to model-check the temporal epistemic logic CTLK.

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The Temporal Logic of Rewriting: A Gentle Introduction

Meseguer

2008

Concurrency, Graphs and Models

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Logiques temporelles basées sur actions pour la vérification des systèmes asynchrones

Cited by 5 publications

References 35 publications

Partial-Order Reduction for Parity Games with an Application on Parameterised Boolean Equation Systems

Partial-Order Reduction for Parity Games with an Application on Parameterised Boolean Equation Systems

Symbolic Model Checking of Logics with Actions

The Temporal Logic of Rewriting: A Gentle Introduction

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