Stuttering for Markov Automata

Abstract

Stutter equivalences are important for system synthesis as well as system analysis. In this paper, we study stutter trace equivalences for Markov automata (MAs) and how they relate to metric temporal logic (MTL) formulas. We first define several variants of stutter trace equivalence for closed MA models. We perform button pushing experiments with a black box model of MA to obtain these equivalences. For every class of MA scheduler, a corresponding variant of stutter trace equivalence is defined. Then we investigate the relationship among these equivalences and also compare them with bisimulation for MAs. Finally, we prove that maximum and minimum probabilities of satisfying properties specified using metric temporal logic (MTL) formulas are preserved under some of these equivalences.