Parameterized Verification of Asynchronous Shared-Memory Systems

Esparza, Javier; Ganty, Pierre; Majumdar, Rupak

doi:10.1007/978-3-642-39799-8_8

Cited by 28 publications

(42 citation statements)

References 26 publications

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“…Hence, FTDAs force us to develop parameterized verification methods. The problem we consider is concerned with parameterized model checking, for which many interesting results exist [14,15,[21][22][23]35]; cf. [7] for a survey.…”

Section: Discussion and Related Workmentioning

confidence: 99%

Para $$^2$$ 2 : parameterized path reduction, acceleration, and SMT for reachability in threshold-guarded distributed algorithms

Konnov

Lazić

Veith

et al. 2017

Form Methods Syst Des

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Automatic verification of threshold-based fault-tolerant distributed algorithms (FTDA) is challenging: FTDAs have multiple parameters that are restricted by arithmetic conditions, the number of processes and faults is parameterized, and the algorithm code is parameterized due to conditions counting the number of received messages. Recently, we introduced a technique that first applies data and counter abstraction and then runs bounded model checking (BMC). Given an FTDA, our technique computes an upper bound on the diameter of the system. This makes BMC complete for reachability properties: it always finds a counterexample, if there is an actual error. To verify state-of-the-art FTDAs, further improvement is needed. In contrast to encoding bounded executions of a counter system over an abstract finite domain in SAT, in this paper, we encode bounded executions over integer counters in SMT. In addition, we introduce a new form of reduction that exploits acceleration and the structure of the FTDAs. This aggressively prunes the execution space to be explored by the solver. In this way, we verified safety of seven FTDAs that were out of reach before.

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Section: Discussion and Related Workmentioning

confidence: 99%

Para $$^2$$ 2 : parameterized path reduction, acceleration, and SMT for reachability in threshold-guarded distributed algorithms

Konnov

Lazić

Veith

et al. 2017

Form Methods Syst Des

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“…In [Esparza et al, 2016], systems with a leader process and arbitrarily many anonymous identical contributors are considered. It provides an analysis of the complexity of the safety verification problem on such systems.…”

Section: Arbitrary Number Of Identical Resourcesmentioning

confidence: 99%

Discrete Parameters in Petri Nets

David

Jard

Lime

et al. 2015

Application and Theory of Petri Nets and Concurrency

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Short abstract:With the aim of increasing the modelling capability of Petri nets, we suggest that models involve parameters to represent the weights of arcs, or the number of tokens in places. We consider the property of coverability of markings. Two general questions arise, the universal and the existential one: "Is there a parameter value for which the property is satisfied?" and "Does the property hold for all possible values of the parameters". We show that these issues are undecidable in the general case. Therefore, we also define subclasses of parameterised nets, depending on whether the parameters are used on places, input or output arcs of transitions. For some classes, we prove that universal and existential coverability become decidable, making these classes more usable in practice. To complete this study, we prove that those problems are ExpSpace-complete. We also address a problem of parameter synthesis, that is computing the set of values for the parameters such that a given marking is coverable in the instantiated net. Restricting parameters to only input weights (preT-PPNs) provides a downward-closed structure to the solution set. We therefore invoke a result for the representation of upward closed set from Valk and Jantzen. The condition to use this procedure is equivalent to decide the universal coverability. We also propose an adaptation of this reasoning to the case of parameters used only as output weights (postT-PPNs). In this case, the condition to use this procedure can be reduced to the decidability of the existential coverability. Finally, we broaden this study by establishing decision frontiers through the study of existential and universal reachability.Keywords: Petri nets -Parameters -Synthesis -Decidability -Complexity -CoverabilityReachability 6 Réseaux de Petri à Paramètres DiscretsRésumé court : Afin de permettre une modélisation plus souple des systèmes, nous proposons d'étendre les réseaux de Petri par des paramètres discrets représentant le poids des arcs ou le nombre de jetons présents dans les places. Dans ce modèle, tout problème de décision peut être décliné sous deux versions, une universelle, demandant si la propriété considérée est vraie quelles que soient les valeurs que prennent les paramètres et une existentielle, qui s'interroge sur l'existence d'une valeur pour les paramètres telle que la propriété soit satisfaite. Concernant la couverture, nous montrons que ces deux problèmes sont indécidables dans le cas général. Nous introduisons donc des sous classes syntaxiques basées sur la restriction des paramètres aux places, aux arcs en sortie ou aux arcs en entrée des transitions. Dans ces di érents cas, nous montrons que la couverture existentielle et universelle sont décidables et EXPSPACE-complètes. Nous étudions alors le problème de la synthèse de paramètres qui s'intéresse à calculer l'ensemble des valeurs de paramètres telles que la propriété considérée soit vraie. Sur les sous classes introduites, concernant la couverture, nous montrons que les ensembles solutions ...

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“…Broadcast networks are a particularly successful model for parameterized verification [36,24,20,21,17,8,12,11,9,6,4]. A broadcast network consists of an arbitrary number of identical finite-state automata communicating via passing messages.…”

Section: Introductionmentioning

confidence: 99%

“…The model was introduced in [24]. The case when the leader and all contributors are finite-state automata was considered in [21] and the corresponding reachability problem was proven to be NP-complete. In [9], the authors took a parameterized complexity look at the reachability problem and proved it fixed-parameter tractable.…”

Section: Introductionmentioning

confidence: 99%

Liveness in Broadcast Networks

2019

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We study two liveness verification problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem is liveness verification. It asks whether there is a computation such that one of the clients visits a final state infinitely often. The complexity of the problem has been open since 2010 when it was shown to be P-hard and solvable in EXPSPACE. We close the gap by a polynomial-time algorithm. The algorithm relies on a characterization of live computations in terms of paths in a suitable graph, combined with a fixed-point iteration to efficiently check the existence of such paths. The second problem is fair liveness verification. It asks for a computation where all participating clients visit a final state infinitely often. We adjust the algorithm to also solve fair liveness in polynomial time.Related Work We already discussed the related work on safety and liveness verification of broadcast networks. Broadcast networks [12,36,20] were introduced to verify ad hoc networks [28,35]. Ad hoc networks are reconfigurable in that the number of clients as well as their communication topology may change during the computation. If the transition relation is compatible with the topology, safety verification has been shown to be decidable [27]. Related studies do not assume compatibility but restrict the topology [26]. If the dependencies among clients are bounded [30], safety verification is decidable independent of the transition relation [38,39]. Verification tools turn these decision procedures into practice [31,15]. D'Osualdo and Ong suggested a typing discipline for the communication topology [16]. In [4], decidability and undecidability results for

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Parameterized Verification of Asynchronous Shared-Memory Systems

Cited by 28 publications

References 26 publications

Para $$^2$$ 2 : parameterized path reduction, acceleration, and SMT for reachability in threshold-guarded distributed algorithms

Para $$^2$$ 2 : parameterized path reduction, acceleration, and SMT for reachability in threshold-guarded distributed algorithms

Discrete Parameters in Petri Nets

Liveness in Broadcast Networks

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