Kobayashi, Naoki and Lago, Ugo Dal and Grellois, Charles - On the Termination Problem for Probabilistic Higher-Order Recursive Programs

lmcs:5919 - Logical Methods in Computer Science, October 2, 2020, Volume 16, Issue 4
On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Authors: Kobayashi, Naoki and Lago, Ugo Dal and Grellois, Charles

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.


Volume: Volume 16, Issue 4
Published on: October 2, 2020
Submitted on: November 23, 2019
Keywords: Computer Science - Programming Languages,Computer Science - Logic in Computer Science


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