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%2F23%3A00134422" target="_blank" >RIV/00216224:14330/23:00134422 - isvavai.cz</a>

Výsledek na webu

<a href="https://dl.acm.org/doi/10.1145/3585391" target="_blank" >https://dl.acm.org/doi/10.1145/3585391</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3585391" target="_blank" >10.1145/3585391</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 a LexRSM not existing even for simple terminating programs. Our contributions are twofold. First, we introduce a generalization of LexRSMs that 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 a LexRSM not existing even for simple terminating programs. Our contributions are twofold. First, we introduce a generalization of LexRSMs that 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

J_imp - Článek v periodiku v databázi Web of Science

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/GA21-24711S" target="_blank" >GA21-24711S: Efektivní analýza a optimalizace pravděpodobnostních systémů a her</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Formal Aspects of Computing

ISSN

0934-5043

e-ISSN

1433-299X

Svazek periodika

35

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

„11:1“-„11:25“

Kód UT WoS článku

001035915800006

EID výsledku v databázi Scopus

2-s2.0-85178022135