Approximate Probabilistic Parallel Multiset Rewriting Using MCMC

Stefan Lüdtke, Max Schröder, Thomas Kirste

Abstract: Probabilistic parallel multiset rewriting systems (PPMRS) model probabilistic, dynamic systems consisting of multiple, (inter-) acting agents and objects (entities), where multiple individual actions can be performed in parallel. The main computational challenge in these approaches is computing the distribution of parallel actions (compound actions), that can be formulated as a constraint satisfaction problem (CSP). Unfortunately, computing the partition function for this distribution exactly is infeasible, as it requires to enumerate all solutions of the CSP, which are subject to a combinatorial explosion. The central technical contribution of this paper is an efficient Markov Chain Monte Carlo (MCMC)-based algorithm to approximate the partition function, and thus the compound action distribution. The proposal function works by performing backtracking in the CSP search tree, and then sampling a solution of the remaining, partially solved CSP. We demonstrate our approach on a Lotka-Volterra system with PPMRS semantics, where exact compound action computation is infeasible. Our approach allows to perform simulation studies and Bayesian filtering with PPMRS semantics in scenarios where this was previously infeasible.