Given Markov chains and Markov decision processes (MDPs) whose transitions are labelled with non-negative integer costs, we study the computational complexity of deciding whether the probability of paths whose accumulated cost satisfies a Boolean combination of inequalities exceeds a given threshold. For acyclic Markov chains, we show that this problem is PP-complete, whereas it is hard for the PosSLP problem and in PSpace for general Markov chains. Moreover, for acyclic and general MDPs, we prove PSpace- and EXP-completeness, respectively. Our results have direct implications on the complexity of computing reward quantiles in succinctly represented stochastic systems.
CITATION STYLE
Haase, C., & Kiefer, S. (2015). The odds of staying on budget. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9135, pp. 234–246). Springer Verlag. https://doi.org/10.1007/978-3-662-47666-6_19
Mendeley helps you to discover research relevant for your work.