eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-12-10
27:1
27:14
10.4230/LIPIcs.FSTTCS.2016.27
article
Model Checking Population Protocols
Esparza, Javier
Ganty, Pierre
Leroux, Jérôme
Majumdar, Rupak
Population protocols are a model for parameterized systems in which a set of identical, anonymous, finite-state processes interact pairwise through rendezvous synchronization. In each step, the pair of interacting processes is chosen by a random scheduler. Angluin et al. (PODC 2004) studied population protocols as a distributed computation model. They characterized the computational power in the limit (semi-linear predicates) of a subclass of protocols (the well-specified ones). However, the modeling power of protocols go beyond computation of semi-linear predicates and they can be used to study a wide range of distributed protocols, such as asynchronous leader election or consensus, stochastic evolutionary processes, or chemical reaction networks. Correspondingly, one is interested in checking specifications on these protocols that go beyond the well-specified computation of predicates.
In this paper, we characterize the decidability frontier for the model checking problem for population protocols against probabilistic linear-time specifications. We show that the model checking problem is decidable for qualitative objectives, but as hard as the reachability problem for Petri nets - a well-known hard problem without known elementary algorithms. On the other hand, model checking is undecidable for quantitative properties.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol065-fsttcs2016/LIPIcs.FSTTCS.2016.27/LIPIcs.FSTTCS.2016.27.pdf
parameterized systems
population protocols
probabilistic model checking
probabilistic linear-time specifications
decidability