Qualitative Reachability for Open Interval Markov Chains
Interval Markov chains extend classical Markov chains with the possibility to describe transition probabilities using intervals, rather than exact values. While the standard formulation of interval Markov chains features closed intervals, previous work has considered also open interval Markov chains, in which the intervals can also be open or half-open. In this paper we focus on qualitative reachability problems for open interval Markov chains, which consider whether the optimal (maximum or minimum) probability with which a certain set of states can be reached is equal to 0 or 1. We present polynomial-time algorithms for these problems for both of the standard semantics of interval Markov chains. Our methods do not rely on the closure of open intervals, in contrast to previous approaches for open interval Markov chains, and can characterise situations in which probability 0 or 1 can be attained not exactly but arbitrarily closely.
- 9.de Alfaro, L.: Formal verification of probabilistic systems. Ph.D. thesis, Stanford University, Department of Computer Science (1997)Google Scholar
- 14.Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: 1991 Proceedings of LICS, pp. 266–277. IEEE Computer Society (1991)Google Scholar
- 17.Puggelli, A., Li, W., Sangiovanni-Vincentelli, A.L., Seshia, S.A.: Polynomial-time verification of PCTL properties of MDPs with convex uncertainties. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 527–542. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_35CrossRefGoogle Scholar
- 20.Sproston, J.: Qualitative reachability for open interval Markov chains. CoRR (2018)Google Scholar
- 21.Vardi, M.: Automatic verification of probabilistic concurrent finite-state programs. In: 1985 Proceedings of FOCS, pp. 327–338. IEEE Computer Society (1985)Google Scholar