On lexicographic proof rules for probabilistic termination
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 probabili...
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| Main Authors: | , , , , |
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| Format: | text |
| Language: | English |
| Published: |
Institutional Knowledge at Singapore Management University
2021
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| Online Access: | https://ink.library.smu.edu.sg/sis_research/9070 https://ink.library.smu.edu.sg/context/sis_research/article/10073/viewcontent/509983_1_En_Print.indd.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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. |
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