Factoring Stochastic Relations

Abstract

When a system represented through a stochastic model is observed, the equivalence of behavior is described through the observation that equivalent inputs lead to equivalent outputs. This paper has a look at the systems that arise when the stochastic model is factored through the congruence. Congruences may re.ne each other, and we show that this re.nement is re.ected through factoring. We also show that factoring a factor does not give rise to any new constructions, since we are kept in the realm of factors for the original system. Thus we cannot have in.nite long chains of factors, so that no new behavior can arise from the original system upon factoring (a system and its factors are bisimilar, after all).