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On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Abstract : In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs. In spite of the emergence of higher-order probabilistic programming languages, not much has been done to combine those two approaches. In this paper, we initiate a study on the probabilistic higher-order model checking problem, by giving some first theoretical and experimental results. As a first step towards our goal, we introduce PHORS, a probabilistic extension of higher-order recursion schemes (HORS), as a model of probabilistic higher-order programs. The model of PHORS may alternatively be viewed as a higher-order extension of recursive Markov chains. We then investigate the probabilistic termination problem-or, equivalently, the probabilistic reachability problem. We prove that almost sure termination of order-2 PHORS is undecidable. We also provide a fixpoint characterization of the termination probability of PHORS, and develop a sound (although possibly incomplete) procedure for approximately computing the termination probability. We have implemented the procedure for order-2 PHORS, and confirmed that the procedure works well through preliminary experiments.
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Submitted on : Monday, January 25, 2021 - 10:48:00 PM
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Naoki Kobayashi, Ugo Dal Lago, Charles Grellois. On the Termination Problem for Probabilistic Higher-Order Recursive Programs. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2020, ⟨10.23638/LMCS-16(4:2)2020⟩. ⟨hal-03120859⟩



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