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 { WS}^3 of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that { 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 { WS}^3 reduce to solving boolean combinations of linear constraints over {mathbb {N}}. This allowed us to develop the first software able to automatically prove correctness for all of the infinitely many possible inputs.
Highlights
We show that the procedures for checking LayeredTermination and StrongConsensus shown in Sect. 4.2, respectively, determine whether a given protocol belongs to WS3; when the protocol does belong to WS3, we can use them to extract a Presburger formula for the predicate computed by the protocol
Recall that Angluin et al have shown that a predicate is computable by a population protocol if and only if it is definable in Presburger arithmetic [2,4]
We have presented WS3, the first class of well-specified population protocols with a membership and correctness problem of reasonable complexity and with the full expressiveness of well-specified protocols
Summary
Population protocols [2,3] are a model of distributed computation by many anonymous finitestate agents. Existing algorithms for the reachability problem are notoriously difficult to implement, and they are considered impractical for most applications For this reason, in this paper we search for a class of well-specified protocols satisfying the following four properties:. Our proofs that the membership and correctness problems belong to DP reduces them to checking (un)satisfiability of two systems of boolean combinations of linear constraints over the natural numbers This allows us to implement our decision procedure on top of the constraint solver Z3 [28], yielding the first software able to automatically prove wellspecification and correctness for all inputs.
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