LTL model checking of interval Markov chains

Abstract

Interval Markov chains (IMCs) generalize ordinary Markov chains by having interval-valued transition probabilities. They are useful for modeling systems in which some transition probabilities depend on an unknown environment, are only approximately known, or are parameters that can be controlled. We consider the problem of computing values for the unknown probabilities in an IMC that maximize the probability of satisfying an ω-regular specification. We give new upper and lower bounds on the complexity of this problem. We then describe an approach based on an expectation maximization algorithm. We provide some analytical guarantees on the algorithm, and show how it can be combined with translation of logic to automata. We give experiments showing that the resulting system gives a practical approach to model checking IMCs. © 2013 Springer-Verlag.