  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.
