Publication Type

Journal Article

Version

publishedVersion

Publication Date

6-2025

Abstract

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.

Keywords

Probabilistic programs, termination, martingales

Discipline

Software Engineering

Research Areas

Intelligent Systems and Optimization

Areas of Excellence

Digital transformation

Publication

Formal Aspects of Computing

Volume

35

Issue

2

First Page

1

Last Page

25

ISSN

0934-5043

Identifier

10.1145/3585391

Publisher

Springer (part of Springer Nature): Springer Open Choice Hybrid Journals

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1145/3585391

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