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On Lexicographic Proof Rules for Probabilistic Termination

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F21%3A00119268" target="_blank" >RIV/00216224:14330/21:00119268 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1007/978-3-030-90870-6_33" target="_blank" >http://dx.doi.org/10.1007/978-3-030-90870-6_33</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/978-3-030-90870-6_33" target="_blank" >10.1007/978-3-030-90870-6_33</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On Lexicographic Proof Rules for Probabilistic Termination

  • Original language description

    We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking supermartingales (LexRSMs). However, LexRSMs introduced in the previous work have a limitation that impedes their automation: all of their components have to be non-negative in all reachable states. This might result in LexRSM not existing even for simple terminating programs. Our contributions are twofold: First, we introduce a generalization of LexRSMs which allows for some components to be negative. This standard feature of non-probabilistic termination proofs was hitherto not known to be sound in the probabilistic setting, as the soundness proof requires a careful analysis of the underlying stochastic process. Second, we present polynomial-time algorithms using our generalized LexRSMs for proving a.s. termination in broad classes of linear-arithmetic programs.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/GJ19-15134Y" target="_blank" >GJ19-15134Y: Verification and Analysis of Probabilistic Programs</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    24th International Symposium on Formal Methods, FM 2021

  • ISBN

    9783030908690

  • ISSN

    0302-9743

  • e-ISSN

  • Number of pages

    21

  • Pages from-to

    619-639

  • Publisher name

    Springer

  • Place of publication

    Cham, Switzerland

  • Event location

    online

  • Event date

    Jan 1, 2021

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

    000758218600033