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A new proof rule for almost-sure termination


Annabelle McIver, Carroll Morgan, Benjamin Kaminski and Joost-Pieter Katoen


RWTH Aachen

Macquarie University


We present a new proof rule for proving almost-sure termination of probabilistic programs, including those that contain demonic non-determinism. An important question for probabilistic programs 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 applies directly to the program's source code, even if the program contains demonic choice. Like others, we use variant functions (a.k.a. "super-martingales") that are real-valued and decrease randomly 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.

BibTeX Entry

    publisher        = {ACM},
    doi              = {10.1145/3158121},
    booktitle        = {Principles of Programming Languages},
    author           = {McIver, Annabelle and Morgan, Carroll and Kaminski, Benjamin and Katoen, Joost-Pieter},
    month            = jan,
    volume           = {2},
    year             = {2018},
    date             = {2018-1-8},
    title            = {{A} new proof rule for almost-sure termination},
    address          = {Los Angeles}


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