Liveness in Broadcast Networks

Chini, Peter; Meyer, Roland; Prakash, Surya

doi:10.1007/978-3-030-31277-0_4

Cited by 10 publications

(10 citation statements)

References 35 publications

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“…Dually, it attempts to find an execution of some population of processes for which a property is violated. Within this context, the complexity of different variants of (parameterized) reachability and repeated coverability have been studied for RBN [12,11,8]. Moreover, many extensions of RBN with clocks, registers and probabilities have been proposed and studied, mainly within the perspective of parameterized verification [10,5,4].…”

Section: Introductionmentioning

confidence: 99%

Reconfigurable Broadcast Networks and Asynchronous Shared-Memory Systems are Equivalent

Balasubramanian

Weil-Kennedy

2021

Electron. Proc. Theor. Comput. Sci.

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We show the equivalence of two distributed computing models, namely reconfigurable broadcast networks (RBN) and asynchronous shared-memory systems (ASMS), that were introduced independently. Both RBN and ASMS are systems in which a collection of anonymous, finite-state processes run the same protocol. In RBN, the processes communicate by selective broadcast: a process can broadcast a message which is received by all of its neighbors, and the set of neighbors of a process can change arbitrarily over time. In ASMS, the processes communicate by shared memory: a process can either write to or read from a shared register. Our main result is that RBN and ASMS can simulate each other, i.e. they are equivalent with respect to parameterized reachability, where we are given two (possibly infinite) sets of configurations C and C ′ defined by upper and lower bounds on the number of processes in each state and we would like to decide if some configuration in C can reach some configuration in C ′ . Using this simulation equivalence, we transfer results of RBN to ASMS and vice versa. Finally, we show that RBN and ASMS can simulate a third distributed model called immediate observation (IO) nets. Moreover, for a slightly stronger notion of simulation (which is satisfied by all the simulations given in this paper), we show that IO nets cannot simulate RBN.

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Section: Introductionmentioning

confidence: 99%

Reconfigurable Broadcast Networks and Asynchronous Shared-Memory Systems are Equivalent

Balasubramanian

Weil-Kennedy

2021

Electron. Proc. Theor. Comput. Sci.

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“…(2) When we project a configuration visited by π (0, ) to Q, we obtain the corresponding configuration of π . We refer to [13] for the detailed construction. Note that client i visits F ¬ϕ infinitely often.…”

Section: Fair Model Checking Inputmentioning

confidence: 99%

“…The paper at hand is an extension of the conference version [12]. It features a new section, namely Sect.…”

Section: Introductionmentioning

confidence: 99%

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Liveness in broadcast networks

2021

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We study liveness and model checking problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem that we consider is Liveness Verification. It asks whether there is a computation such that one clients visits a final state infinitely often. The complexity of the problem has been open. It was shown to be $$\texttt {P}$$ P -hard but in $$\texttt {EXPSPACE}$$ EXPSPACE . We close the gap by a polynomial-time algorithm. The latter 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. Both problems can be instrumented to answer model checking questions for broadcast networks against linear time temporal logic specifications. The first problem in this context is Fair Model Checking. It demands that for all computations of a broadcast network, all participating clients satisfy the specification. We solve the problem via the Vardi–Wolper construction and a reduction to Liveness Verification. The second problem is Sparse Model Checking. It asks whether each computation has a participating client that satisfies the specification. We reduce the problem to Fair Liveness Verification.

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“…Dually, it can be viewed as the problem of finding an execution of some number of agents which violates a given property. Ever since their introduction within this context [10], RBN have been studied extensively, with various results on (parameterized) reachability and coverability [8,10,3,7], along with various extensions using probabilities and clocks [5,4].…”

Section: Introductionmentioning

confidence: 99%

Parameterized Analysis of Reconfigurable Broadcast Networks (Long Version)

Balasubramanian¹,

Lucie²,

Weil-Kennedy³

2022

Preprint

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Reconfigurable broadcast networks (RBN) are a model of distributed computation in which agents can broadcast messages to other agents using some underlying communication topology which can change arbitrarily over the course of executions. In this paper, we conduct parameterized analysis of RBN. We consider cubes, (infinite) sets of configurations in the form of lower and upper bounds on the number of agents in each state, and we show that we can evaluate boolean combinations over cubes and reachability sets of cubes in PSPACE. In particular, reachability from a cube to another cube is a PSPACE-complete problem. To prove the upper bound for this parameterized analysis, we prove some structural properties about the reachability sets and the symbolic graph abstraction of RBN, which might be of independent interest. We justify this claim by providing two applications of these results. First, we show that the almost-sure coverability problem is PSPACE-complete for RBN, thereby closing a complexity gap from a previous paper [3]. Second, we define a computation model using RBN, à la population protocols, called RBN protocols. We characterize precisely the set of predicates that can be computed by such protocols.

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Liveness in Broadcast Networks

Cited by 10 publications

References 35 publications

Reconfigurable Broadcast Networks and Asynchronous Shared-Memory Systems are Equivalent

Reconfigurable Broadcast Networks and Asynchronous Shared-Memory Systems are Equivalent

Liveness in broadcast networks

Parameterized Analysis of Reconfigurable Broadcast Networks (Long Version)

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