Checking Qualitative Liveness Properties of Replicated Systems with Stochastic Scheduling
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Proceedings |
| Conference | Computer Aided Verification, CAV 2020 |
| MU Faculty or unit | |
| Citation | BLONDIN, Michael, Javier ESPARZA, Martin HELFRICH, Antonín KUČERA and Philipp MEYER. Checking Qualitative Liveness Properties of Replicated Systems with Stochastic Scheduling. In Shuvendu K. Lahiri, Chao Wang. Computer Aided Verification, CAV 2020. Cham, Německo: Springer International Publishing, 2020, p. 372-397. ISBN 978-3-030-53290-1. Available from: https://dx.doi.org/10.1007/978-3-030-53291-8_20. |
| web | https://doi.org/10.1007/978-3-030-53291-8_20 |
| Doi | http://dx.doi.org/10.1007/978-3-030-53291-8_20 |
| Keywords | Replicated systems; population protocols |
| Description | We present a sound and complete method for the verification of qualitative liveness properties of replicated systems under stochastic scheduling. These are systems consisting of a finite-state program, executed by an unknown number of indistinguishable agents, where the next agent to make a move is determined by the result of a random experiment. We show that if a property of such a system holds, then there is always a witness in the shape of a Presburger stage graph: a finite graph whose nodes are Presburger-definable sets of configurations. Due to the high complexity of the verification problem (non-elementary), we introduce an incomplete procedure for the construction of Presburger stage graphs, and implement it on top of an SMT solver. The procedure makes extensive use of the theory of well-quasi-orders, and of the structural theory of Petri nets and vector addition systems. We apply our results to a set of benchmarks, in particular to a large collection of population protocols, a model of distributed computation extensively studied by the distributed computing community. |
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