Playing with Probabilities in Reconfigurable Broadcast Networks

Bertrand, Nathalie; Fournier, Paulin; Sangnier, Arnaud

doi:10.1007/978-3-642-54830-7_9

Cited by 20 publications

(19 citation statements)

References 14 publications

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“…Continuous-time parametric and probabilistic models have also been considered in some very restricted settings [9]. Networks of probabilistic processes where the number of processes is a parameter have also been studied in [4,5], and probabilistic timed automata with parameters in clock constraints and invariants have been studied in [1].…”

Section: Introductionmentioning

confidence: 99%

Parameter Synthesis for Parametric Interval Markov Chains

Delahaye

Lime

Petrucci

2015

Lecture Notes in Computer Science

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Abstract. Interval Markov Chains (IMCs) are the base of a classic probabilistic specification theory introduced by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In this paper we study parameter synthesis for a parametric extension of Interval Markov Chains in which the endpoints of intervals may be replaced with parameters. In particular, we propose constructions for the synthesis of all parameter values ensuring several properties such as consistency and consistent reachability in both the existential and universal settings with respect to implementations. We also discuss how our constructions can be modified in order to synthesise all parameter values ensuring other typical properties.

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Section: Introductionmentioning

confidence: 99%

Parameter Synthesis for Parametric Interval Markov Chains

Delahaye

Lime

Petrucci

2015

Lecture Notes in Computer Science

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“…Networks with communication failures were considered in [14]. Probabilistic broadcast networks were studied in [5]. In [6], a variant of broadcast networks was considered where the clients follow a local strategy.…”

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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“…Perhaps surprisingly, this modification not only allows for a more faithful modelling of MANETs, but it also leads to decidability of both the coverability and the synchronization problems [6]. A probabilistic extension of reconfigurable broadcast networks has been studied in [1,2] to model randomized protocols.…”

Section: Introductionmentioning

confidence: 99%

Parameterized Verification of Synchronization in Constrained Reconfigurable Broadcast Networks

Balasubramanian

Bertrand

Markey

2018

Tools and Algorithms for the Construction and Analysis of Systems

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Reconfigurable broadcast networks provide a convenient formalism for modelling and reasoning about networks of mobile agents broadcasting messages to other agents following some (evolving) communication topology. The parameterized verification of such models aims at checking whether a given property holds irrespective of the initial configuration (number of agents, initial states and initial communication topology). We focus here on the synchronization property, asking whether all agents converge to a set of target states after some execution. This problem is known to be decidable in polynomial time when no constraints are imposed on the evolution of the communication topology (while it is undecidable for static broadcast networks). In this paper we investigate how various constraints on reconfigurations affect the decidability and complexity of the synchronization problem. In particular, we show that when bounding the number of reconfigured links between two communications steps by a constant, synchronization becomes undecidable; on the other hand, synchronization remains decidable in PTIME when the bound grows with the number of agents.

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Playing with Probabilities in Reconfigurable Broadcast Networks

Abstract: International audienc

Cited by 20 publications

References 14 publications

Parameter Synthesis for Parametric Interval Markov Chains

Parameter Synthesis for Parametric Interval Markov Chains

Liveness in Broadcast Networks

Parameterized Verification of Synchronization in Constrained Reconfigurable Broadcast Networks

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