Towards Efficient Verification of Population Protocols

Abstract

Population protocols are a well established model of computation by anonymous, identical finite state agents. A protocol is well-specified if from every initial configuration, all fair executions reach a common consensus. The central verification question for population protocols is the well-specification problem: deciding if a given protocol is well-specified. Esparza et al. have recently shown that this problem is decidable, but with very high complexity: it is at least as hard as the Petri net reachability problem, which is EXPSPACE-hard, and for which only algorithms of non-primitive recursive complexity are currently known. In this paper we introduce the class WS3 of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that WS3 has the same computational power as general well-specified protocols, and captures standard protocols from the literature. Moreover, we show that the membership problem for WS3 reduces to solving boolean combinations of linear constraints over N. This allowed us to develop the first software able to automatically prove well-specification for all of the infinitely many possible inputs.Comment: 27 pages, 1 figur

Peregrine: A Tool for the Analysis of Population Protocols

“…Peregrine implements the approach of [6] to verify correctness of protocols which are silent. A protocol is said to be silent if from every initial configuration, every fair execution leads to a terminal configuration.…”

“…The majority protocol of Sect. 2 and most existing protocols from the literature are silent [6]. We briefly describe the approach of [6] and how it is integrated into Peregrine.…”

“…The analysis features of Peregrine include manual stepby-step simulation; automatic sampling; statistics generation of average convergence speed; detection of incorrect executions through simulation; and formal verification of correctness. The first four features are supported for all protocols, while verification is supported for silent protocols, a large subclass of protocols [6]. Verification is performed automatically over all of the infinitely many initial configurations using the recent approach of [6] for solving the so-called well-specification problem.…”

“…The first four features are supported for all protocols, while verification is supported for silent protocols, a large subclass of protocols [6]. Verification is performed automatically over all of the infinitely many initial configurations using the recent approach of [6] for solving the so-called well-specification problem.…”

“…The verification algorithm of Peregrine is based on [6], where a novel approach for the parameterized verification of silent population protocols has been presented. The command-line tool of [6] only offers support for proving correctness, with no functionality for visualization or simulation. Further, contrary to Peregrine, the tool cannot produce counterexamples when correctness fails.…”