Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th