Timed Comparisons of Semi-Markov Processes
Abstract
Semi-Markov processes are Markovian processes in which the firing time of the 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.
Cite
@article{arxiv.1711.10216,
title = {Timed Comparisons of Semi-Markov Processes},
author = {Mathias Ruggaard Pedersen and Nathanaël Fijalkow and Giorgio Bacci and Kim Guldstrand Larsen and Radu Mardare},
journal= {arXiv preprint arXiv:1711.10216},
year = {2017}
}