Abstract
This paper studies the linear time-branching time spectrum of equivalences for a subclass of interactive Markov chains (IMCs) that are not subject to any further synchronization. This subclass of IMCs is known as closed 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 closed IMCs. Next, we define several variants of stutter trace equivalence for closed IMCs. We perform button pushing experiments with stutter insensitive stochastic trace machines to obtain these equivalences. We investigate the relationship among these stutter trace equivalences and also compare them with weak bisimulation for closed IMCs. We discuss the relation between several strong and weak trace equivalences defined in this paper. Next, we use these results to sketch the linear time-branching time spectrum of equivalences for IMCs. Finally, we prove that maximum and minimum probabilities of satisfying properties specified using metric temporal logic (MTL) formulas are preserved under some of these trace and stutter trace equivalences.
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