The Linear Time-Branching Time Spectrum of Equivalences for Stochastic Systems with Non-determinism

Abstract

This paper studies linear time-branching time spectrum of equivalences for interactive Markov chains (IMCs). We define several variants of trace equivalence by performing button pushing experiments on stochastic trace machines. We establish the relation between these equivalences and also compare them with bisimulation for IMCs. Next, we define several variants of stutter trace equivalence for IMCs. We perform button pushing experiments with stutter insensitive stochastic trace machines to obtain these equivalences. We investigate the relationship among these stutter equivalences and also compare them with weak bisimulation for IMCs. Finally, we discuss the relation between several strong and weak equivalences defined in this paper.