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.
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