A notion of congruence for dtsPBC

Algebra dtsPBC is a discrete time stochastic extension of finite Petri box calculus (PBC) enriched with iteration. In this paper, we define a number of stochastic equivalences for dtsPBC which allow one to identify finite and infinite stochastic processes with similar behaviour. A problem of preservation of the equivalences by algebraic operations is discussed. As a result, we construct an equivalence that is a congruence relation.