On Lexicographic Proof Rules for Probabilistic Termination

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On Lexicographic Proof Rules for Probabilistic Termination

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Lexicographic Proof Rules for Probabilistic Termination

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GJ19-15134Y" target="_blank" >GJ19-15134Y: Verifikace a analýza pravděpodobnostních programů</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název statě ve sborníku

24th International Symposium on Formal Methods, FM 2021

ISBN

9783030908690

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

21

Strana od-do

619-639

Název nakladatele

Springer

Místo vydání

Cham, Switzerland

Místo konání akce

online

Datum konání akce

1. 1. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000758218600033