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Register a new userA new rule for almost-certain termination of probabilistic- and demonic programs
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Added by
Carroll Morgan
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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Extending our own and others earlier approaches to reasoning about termination of probabilistic programs, we propose and prove a new rule for termination with probability one, also known as almost-certain termination. The rule uses both (non-strict) super martingales and guarantees of progress, together, and it seems to cover significant cases that earlier methods do not. In particular, it suffices for termination of the unbounded symmetric random walk in both one- and two dimensions: for the first, we give a proof; for the second, we use a theorem of Foster to argue that a proof exists. Non-determinism (i.e. demonic choice) is supported; but we do currently restrict to discrete distributions.
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An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates almost surely. Proving that can be hard, and this paper presents a new method for doing so; it is expressed in a program logic, and so applies directly to source code. The programs may contain both probabilistic- and demonic choice, and the probabilistic choices may depend on the current state. As do other researchers, we use variant functions (a.k.a. super-martingales) that are real-valued and probabilistically might decrease on each loop iteration; but our key innovation is that the amount as well as the probability of the decrease are parametric. We prove the soundness of the new rule, indicate where its applicability goes beyond existing rules, and explain its connection to classical results on denumerable (non-demonic) Markov chains.
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