Verification of Directed Acyclic Ad Hoc Networks

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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“…, q ′ k ) be another configuration with k clients and a ∈ D a message. We have a transition c a − → N c ′ if the following conditions hold: (1)…”

Section: Broadcast Networkmentioning

confidence: 99%

Liveness in Broadcast Networks

2019

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“…There is an MSO-formula chr C with k free first-order variables such that, for every r -topology G = (V, E,T ) with T 1 = {init} and g 1 …”

Section: Mso-definable Topologies Of Bounded Clique-widthmentioning

confidence: 99%

“…Although the PMCP is undecidable in general (see [28,52]) it becomes decidable for some combinations of communication primitives, network topologies, and specification languages, e.g., [1,8,14,21,22,30,51]. Often, it is proved decidable by a reduction to model checking finitely many finite-state systems [2,16,24,28,36].…”

Section: Introductionmentioning

confidence: 99%

“…Such a number is known as a cutoff for the given parameterized system. 1 In other cases the reduction produces a single finite-state system, often in the form of a fair transition system (such as a Büchi automaton), that represents the set of all execution traces of systems of all sizes. Note that PMCP is at least as hard as ordinary model checking since one can consider a replicated process that does not communicate with any others.…”

Section: Introductionmentioning

confidence: 99%

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Parameterized model checking of rendezvous systems

et al. 2017

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Parameterized model checking is the problem of deciding if a given formula holds irrespective of the number of participating processes. A standard approach for solving the parameterized model checking problem is to reduce it to model checking finitely many finite-state systems. This work considers the theoretical power and limitations of this technique. We focus on concurrent systems in which processes communicate via pairwise rendezvous, as well as the special cases of disjunctive guards and token passing; specifications are expressed in indexed temporal logic without the next operator; and the underlying network topologies are generated by suitable formulas and graph operations. First, we settle the exact computational complexity of the parameterized model checking problem for some of our concurrent systems, and establish new decidability results for others. Second, we consider the cases where model checking the parameterized system can be reduced to model checking some fixed number of processes, the number is known as a cutoff. We provide many cases for when such cutoffs can be computed, establish lower bounds on the size of such cutoffs, and identify cases where no cutoff exists. Third, we consider cases for which the parameterized system is equivalent to a single finite-state system (more precisely a Büchi word automaton), and establish tight bounds on the sizes of such automata.

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“…Coverability for GTS is studied in [8] where it was proved that it is decidable for bounded path graphs ordered via subgraph inclusion. A model with topologies represented as acyclic directed graphs has been presented in [1]. Coverability for automata-based models of broadcast communication has recently been studied in [15,16,13,18,12].…”

Section: Conclusion and Related Workmentioning

confidence: 99%

Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations

Delzanno

Stückrath

2014

Lecture Notes in Computer Science

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We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be transformed by the rule as well. For the new class for graph rewrite rules, we provide a symbolic procedure working on minimal representations of upward closed sets of configurations. We prove correctness and effectiveness of the procedure by a categorical presentation of rewrite rules as well as the involved order, and using results for well-structured transition systems. We apply the resulting procedure to the analysis of the Distributed Dining Philosophers protocol on an arbitrary network structure.

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Verification of Directed Acyclic Ad Hoc Networks

Cited by 11 publications

References 14 publications

Liveness in Broadcast Networks

Liveness in Broadcast Networks

Parameterized model checking of rendezvous systems

Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations

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