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 of the protocol 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 TOWER-hard, and for which only algorithms of non-primitive recursive complexity are currently known. In this paper we introduce the class ${\mathrm{WS}}^3$ of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that ${\mathrm{WS}}^3$ has the same computational power as general well-specified protocols, and captures standard protocols from the literature. Moreover, we show that the membership and correctness problems for ${\mathrm{WS}}^3$ reduce to solving boolean combinations of linear constraints over $N$ . This allowed us to develop the first software able to automatically prove correctness for all of the infinitely many possible inputs.