Reachability in Networks of Register Protocols under Stochastic Schedulers

Bouyer, Patricia; Markey, Nicolas; Randour, Mickaël; Stan, Daniel

doi:10.4230/lipics.icalp.2016.106

Cited by 10 publications

(18 citation statements)

References 13 publications

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“…The second model that we consider is a formal model of asynchronous shared-memory systems (ASMS) [13,7,6]. In this model, we have a collection of anonymous, finite-state processes executing the same protocol, and a single register which all processes can access to perform a read/write operation.…”

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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“…Finally, by the reduction given in ( [3], Section 4.2), our results on cubereachability and almost-sure coverability can be transferred to another model of distributed computation called asynchronous shared memory systems (ASMS), giving a PSPACE-completeness result for both of these problems. This solves an open problem from ( [6], Section 6).…”

Section: Introductionmentioning

confidence: 87%

“…Similar to the cube-reachability problem, our result on almost-sure coverability also applies to the related model of ASMS. This solves an open problem from [6]. For lack of space, we once again defer this discussion to the appendix.…”

Section: Pspace-completeness Of the Almost-sure Coverability Problemmentioning

confidence: 96%

“…To summarize, we have shown that many important parameterized problems of RBN can be solved in PSPACE, that the sub-problem of the cube-reachability problem defined in [8] can be generalized while retaining the same upper bounds, and that the almost-sure coverability problems for RBN and ASMS are PSPACEcomplete, thereby solving open problems from [3,6]. We believe that our other results might be of independent interest, and we provide an application by introducing RBN protocols and characterizing the set of predicates that they can compute.…”

Section: Introductionmentioning

confidence: 93%

“…Now, similar to RBN, it is easy to define the notion of a cut-off for ASMS. The following fact is known (Theorem 3 of [6]).…”

Section: The Almost-sure Coverability Problemmentioning

confidence: 99%

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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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Parameterized Analysis of Reconfigurable Broadcast Networks

Balasubramanian

Lucie

Weil-Kennedy

2022

Lecture Notes in Computer Science

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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 . In particular, reachability from a cube to another cube is a -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 -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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Reachability in Networks of Register Protocols under Stochastic Schedulers

Cited by 10 publications

References 13 publications

Reconfigurable Broadcast Networks and Asynchronous Shared-Memory Systems are Equivalent

Reconfigurable Broadcast Networks and Asynchronous Shared-Memory Systems are Equivalent

Parameterized Analysis of Reconfigurable Broadcast Networks (Long Version)

Parameterized Analysis of Reconfigurable Broadcast Networks

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