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Communication Dans Un Congrès Année : 2019

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Résumé

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 PHORSs, and confirmed that the procedure works well through preliminary experiments.
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Dates et versions

hal-02399361 , version 1 (09-12-2019)

Identifiants

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Naoki Kobayashi, Ugo Dal Lago, Charles Grellois. On the Termination Problem for Probabilistic Higher-Order Recursive Programs. LICS 2019 - 34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, France. pp.1-14, ⟨10.1109/LICS.2019.8785679⟩. ⟨hal-02399361⟩
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