Verification of Immediate Observation Population Protocols

TL;DR

This paper studies immediate observation population protocols, showing that the problems of protocol correctness and predicate computation are decidable in exponential space, providing a more efficient analysis method for this class.

Contribution

The paper proves that for IO population protocols, correctness and predicate computation problems are decidable in exponential space, avoiding Petri net reachability complexity.

Findings

Decidability of correctness and predicate computation in exponential space for IO protocols.

First class of protocols with algorithms not relying on Petri net reachability.

Provides a practical analysis approach for a significant class of population protocols.

Abstract

Population protocols (Angluin et al., PODC, 2004) are a formal model of sensor networks consisting of identical mobile devices. Two devices can interact and thereby change their states. Computations are infinite sequences of interactions satisfying a strong fairness constraint. A population protocol is well-specified if for every initial configuration $C$ of devices, and every computation starting at $C$, all devices eventually agree on a consensus value depending only on $C$. If a protocol is well-specified, then it is said to compute the predicate that assigns to each initial configuration its consensus value. In a previous paper we have shown that the problem whether a given protocol is well-specified and the problem whether it computes a given predicate are decidable. However, in the same paper we prove that both problems are at least as hard as the reachability problem for Petri nets. Since all known algorithms for Petri net reachability have non-primitive recursive complexity, in this paper we restrict attention to immediate observation (IO) population protocols, a class introduced and studied in (Angluin et al., PODC, 2006). We show that both problems are solvable in exponential space for IO protocols. This is the first syntactically defined, interesting class of protocols for which an algorithm not requiring Petri net reachability is found.