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7 - Termination Analysis of Probabilistic Programs with Martingales

Published online by Cambridge University Press:  18 November 2020

By
Krishnendu Chatterjee ,
Hongfei Fu  and
Petr Novotný
Edited by
Gilles Barthe ,
Joost-Pieter Katoen  and
Alexandra Silva
Gilles Barthe
Affiliation:
Max Planck Institute for Security and Privacy
Joost-Pieter Katoen
Affiliation:
RWTH Aachen University, Germany
Alexandra Silva
Affiliation:
University College London
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Summary

For non-probabilistic programs, a key question in static analysis is termination, which asks whether a given program terminates under a given initial condition. In the presence of probabilistic behaviour, there are two fundamental extensions of the termination question: (a) the almost-sure termination question, which asks whether the termination probability is 1; and (b) the bounded-time termination question, which asks whether the expected termination time is bounded. There are many active research directions to address these two questions; one important such direction is the use of martingale theory for termination analysis. In this chapter, we survey the main techniques of the martingale-based approach to the termination analysis of probabilistic programs.

Keywords

Almost-sure terminationbounded terminationranking supermartingales
Type
Chapter
Information
Foundations of Probabilistic Programming , pp. 221 - 258
Publisher: Cambridge University Press
Print publication year: 2020
Creative Commons
Creative Common License - CCCreative Common License - BY
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY 4.0 https://creativecommons.org/cclicenses/

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