On Lexicographic Proof Rules for Probabilistic Termination

Result code in 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>
Result on the web
<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>

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 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA21-24711S" target="_blank" >GA21-24711S: Efficient Analysis and Optimization for Probabilistic Systems and Games</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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