Semi-Markov processes are Markovian processes in which the firing time of transitions is modelled by probabilistic distributions over positive reals interpreted as the probability of firing a transition at a certain moment in time. In this paper we consider the trace-based semantics of semi-Markov processes, and investigate the question of how to compare two semi-Markov processes with respect to their time-dependent behaviour. To this end, we introduce the relation of being “faster than” between processes and study its algorithmic complexity. Through a connection to probabilistic automata we obtain hardness results showing in particular that this relation is undecidable. However, we present an additive approximation algorithm for a time-bounded variant of the faster-than problem over semi-Markov processes with slow residence-time functions, and a coNP algorithm for the exact faster-than problem over unambiguous semi-Markov processes.
CITATION STYLE
Pedersen, M. R., Fijalkow, N., Bacci, G., Larsen, K. G., & Mardare, R. (2018). Timed Comparisons of Semi-Markov Processes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10792 LNCS, pp. 271–283). Springer Verlag. https://doi.org/10.1007/978-3-319-77313-1_21
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