On the Termination Problem for Probabilistic Higher-Order Recursive Programs

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 o...

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Bibliographic Details
Published in:Logical methods in computer science Vol. 16, Issue 4
Main Authors: Kobayashi, Naoki, Lago, Ugo Dal, Grellois, Charles
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science Association 02.10.2020
Logical Methods in Computer Science e.V
Subjects:
Computer Science
computer science - logic in computer science
computer science - programming languages
Logic in Computer Science
model checking
probabilistic programs
higher-order programs
termination probabilities
ISSN:1860-5974, 1860-5974
Online Access:Get full text
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Summary: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.
ISSN:1860-5974
1860-5974
DOI:10.23638/LMCS-16(4:2)2020