[KPR16] Nishanthan Kamaleson, David Parker and Jonathan E. Rowe. Finite-Horizon Bisimulation Minimisation for Probabilistic Systems. In Proc. 2016 International Symposium on Model Checking of Software (SPIN'16), volume 9641 of LNCS, pages 147-164, Springer. April 2016. [pdf] [bib] [Proposes a finite-horizon variant of probabilistic bisimulation and implements various associated minimisation algorithms in an extension of PRISM.]
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Abstract. We present model reduction techniques to improve the efficiency and scalability of verifying probabilistic systems over a finite time horizon. We propose a finite-horizon variant of probabilistic bisimulation for discrete-time Markov chains, which preserves a bounded fragment of the temporal logic PCTL. In addition to a standard partition-refinement based minimisation algorithm, we present on-the-fly finite-horizon minimisation techniques, which are based on a backwards traversal of the Markov chain, directly from a high-level model description. We investigate both symbolic and explicit-state implementations, using SMT solvers and hash functions, respectively, and implement them in the PRISM model checker. We show that finite-horizon reduction can provide significant reductions in model size, in some cases outperforming PRISM's existing efficient implementations of probabilistic verification.