Model-checking CTL* over flat Presburger counter systems

Demri, Stéphane; Finkel, Alain; Goranko, Valentin; Drimmelen, Govert van

doi:10.3166/jancl.20.313-344

Cited by 20 publications

(47 citation statements)

References 54 publications

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“…Due to Lemma 1, henceforth we consider only non-blocking flat counter systems. Since the reachability relation is definable in (PA) for flat counter systems [10], it is even possible to decide whether all maximal runs from a given configuration are infinite.…”

Section: Introductionmentioning

confidence: 99%

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Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic

Demri

Dhar

2014

Lecture Notes in Computer Science

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Abstract. We show that model-checking flat counter systems over CTL* (with arithmetical constraints on counter values) has the same complexity as the satisfiability problem for Presburger arithmetic. The lower bound already holds with the temporal operator EF only, no arithmetical constraints in the logical language and with guards on transitions made of simple linear constraints. This complements our understanding of model-checking flat counter systems with linear-time temporal logics, such as LTL for which the problem is already known to be (only) NP-complete with guards restricted to the linear fragment.

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Section: Introductionmentioning

confidence: 99%

“…We know that MC(CTL * , FlatCS) is decidable [10] but its exact complexity is not fully characterized (actually, this is the purpose of the present paper). The restriction to LTL formulae is known to be NP-complete [8] when guards are restricted to the linear fragment.…”

Section: Introductionmentioning

confidence: 99%

Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic

Demri

Dhar

2014

Lecture Notes in Computer Science

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“…The use of Presburger constraints has been widely adopted in verification of counter systems, for example in works of Fribourg et al [36], Bultan et al [21], Bardin et al [14], Demri et al [30]. Presburger arithmetic on integers seems to be suitable for describing systems with an infinite state space because of having counters with unbounded integer domains.…”

Section: Related Workmentioning

confidence: 99%

Automatic Verification of Parameterized Systems by Over-Approximation

Jahundovics¹

2015

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This thesis presents a completely automatic verification framework to check safety properties of parameterized systems. A parameterized system is a family of finite state systems where every system consists of a finite number of processes running in parallel the same algorithm. All the systems in the family differ only in the number of the processes and, in general, the number of systems in a family may be unbounded. Examples of parameterized systems are communication protocols, mutual exclusion protocols, cache coherence protocols, distributed algorithms etc.Model-checking of finite state systems is a well-developed formal verification approach of proving properties of systems in an automatic way. However, it cannot be applied directly to parameterized systems because the unbounded number of systems in a family means an infinite state space. In this thesis we propose to abstract an original family of systems consisting of an unbounded number of processes into one consisting of a fixed number of processes. An abstracted system is considered to consist of k + 1 components -k reference processes and their environment. The transition relation for the abstracted system is an over-approximation of the transition relation for the original system, therefore, a set of reachable states of the abstracted system is an over-approximation of the set of reachable states of the original one.A safety property is considered to be parameterized by a fixed number of processes whose relationship is in the center of attention in the property. Such processes serve as reference processes in the abstraction. We propose an encoding which allows to perform reachability analysis for an abstraction parameterized by the reference processes.We have successfully verified three classic parameterized systems with replicated processes by applying this method.

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“…Even though it is not difficult to generate path schemas in a fair and complete way by tracing the transitions, the details of the enumeration are quite important but often underestimated, see e.g.. [BFLS05,DFGvD10] (see some exception in [Ler03]). First, we want an enumeration strategy that is efficient in practice.…”

Section: Why Path Schema Enumeration?mentioning

confidence: 99%

“…A Presburger counter system C = Q, n, δ is a structure (see e.g. [DFGvD10,Ler12]) such that -Q is a nonempty finite set of control states, -n ≥ 1 is the dimension of the system, i.e. the number of counters, we assume that the counters are represented by the variables x 1 , .…”

Section: Presburger Counter Systemsmentioning

confidence: 99%

Witness Runs for Counter Machines

Barrett

Demri

Deters

2013

Frontiers of Combining Systems

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Abstract. In this paper, we present recent results about the verification of counter machines by using decision procedures for Presburger arithmetic. We recall several known classes of counter machines for which the reachability sets are Presburger-definable as well as temporal logics with arithmetical constraints. We discuss issues related to flat counter machines, path schema enumeration, and the use of SMT solvers.

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Model-checking CTL* over flat Presburger counter systems

Cited by 20 publications

References 54 publications

Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic

Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic

Automatic Verification of Parameterized Systems by Over-Approximation

Witness Runs for Counter Machines

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