Maximally Parallel Probabilistic Semantics for Multiset Rewriting

Maximally parallel semantics have been proposed for many formalisms as an alternative to the standard interleaving semantics for some modelling scenarios. Nevertheless, in the probabilistic setting an affirmed interpretation of maximal parallelism still lacks. We define a synchronous maximally parallel probabilistic semantics for multiset rewriting tailored to describe, simulate and verify biological systems evolving with maximally parallel steps. Each step of the proposed semantics is parallel as each reaction can happen multiple times, and it is maximal as it leaves no enabled reaction i.e. as many reactions as possible are executed. We define a maximally parallel probabilistic semantics in terms of Discrete Time Markov Chain for systems described by stochastic multiset rewriting. We propose a simple, maximally parallel, model of Caenorhabditis elegans vulval development on which we show probabilistic simulations results.