# Towards Efficient Verification of Population Protocols

## TL;DR

This paper introduces the WS3 class of protocols, enabling efficient automatic verification of well-specified population protocols by reducing the problem to solving boolean combinations of linear constraints.

## Contribution

It defines the WS3 class, proves its computational equivalence to general protocols, and develops the first software for automatic verification of well-specification.

## Key findings

- WS3 captures standard protocols from literature
- Membership problem reduces to solving linear constraints
- Software can automatically verify well-specification

## 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.