Timed Comparisons of Semi-Markov Processes

  • Mathias R. Pedersen
  • Nathanaël Fijalkow
  • Giorgio Bacci
  • Kim G. Larsen
  • Radu Mardare
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10792)


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 \(\mathbf {coNP}\) algorithm for the exact faster-than problem over unambiguous semi-Markov processes.


Automata for system analysis and programme verification Real-time systems Semi-Markov processes Probabilistic automata 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceAalborg UniversityAalborgDenmark
  2. 2.The Alan Turing InstituteLondonUK

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