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arXiv · 1811.02133

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Naoki Kobayashi·Ugo Dal Lago·Charles Grellois
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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 (but 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 that are reported at the end of the article.

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Naoki Kobayashi, Ugo Dal Lago, Charles Grellois. 2026-08-19. On the Termination Problem for Probabilistic Higher-Order Recursive Programs. https://doi.org/10.23638/lmcs-16(4%3A2)2020

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