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.

人口协议是由匿名、相同的有限状态代理建立的计算模型。如果从每个初始配置中，协议的所有公平执行都达成共识，则协议是明确指定的。种群协议的中心验证问题是井规范问题：确定给定的协议是否是规范的。埃斯帕扎等人。最近表明这个问题是可判定的，但具有非常高的复杂性：它至少与 Petri 网可达性问题一样困难，这是TOWER困难的，并且目前只知道非原始递归复杂性的算法。在本文中，我们介绍类\({ WS}^3\)明确指定的强静默协议，我们证明它适用于自动验证。更准确地说，我们表明\({ WS}^3\)具有与一般明确指定的协议相同的计算能力，并从文献中捕获标准协议。此外，我们表明\({ WS}^3\)的隶属度和正确性问题简化为解决\({\mathbb {N}}\)上线性约束的布尔组合。这使我们能够开发出第一个能够自动证明所有无限可能输入的正确性的软件。