On Stochastic Rewriting and Combinatorics via Rule-Algebraic Methods

TL;DR

This paper develops rule-algebraic methods to analyze stochastic rewriting systems, connecting continuous-time Markov chains with combinatorial generating functions for static analysis.

Contribution

It introduces new generating function techniques for static analysis of stochastic rewriting systems within a rule-algebraic framework.

Findings

Establishes relationships between continuous-time and discrete-time Markov chains in rewriting systems.

Develops generating function methods for pattern-counting observables.

Provides tools for static analysis of stochastic rewriting systems.

Abstract

Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting systems described in terms of continuous-time Markov chains, their embedded discrete-time Markov chains and certain types of generating function expressions in combinatorics. We introduce a number of generating function techniques that permit a novel form of static analysis for rewriting systems based upon marginalizing distributions over the states of the rewriting systems via pattern-counting observables.