Lexicographic ranking supermartingales: an efficient approach to termination of probabilistic programs

AGRAWAL, Sheshansh, Krishnendu CHATTERJEE a Petr NOVOTNÝ. Lexicographic ranking supermartingales: an efficient approach to termination of probabilistic programs. In PACMPL (Proceedings of POPL'18). New York, NY, USA: ACM, 2018, s. "34:1--34:32", 32 s. ISSN 2475-1421.

Základní údaje

Originální název

Lexicographic ranking supermartingales: an efficient approach to termination of probabilistic programs

Autoři

AGRAWAL, Sheshansh, Krishnendu CHATTERJEE a Petr NOVOTNÝ

Vydání

New York, NY, USA, PACMPL (Proceedings of POPL'18), od s. "34:1--34:32", 32 s. 2018

Nakladatel

ACM

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Další údaje

Typ výsledku

Stať ve sborníku

Utajení

není předmětem státního či obchodního tajemství

ISSN

Klíčová slova anglicky

probabilistic termination; ranking functions; supermartingales

Příznaky

Mezinárodní význam, Recenzováno

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Anotace

V originále

Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure) termination problem asks whether a given program program terminates with probability 1. While ranking functions provide a sound and complete method for non-probabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). Although deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to programs of restricted control-flow structure. For non-probabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of real-world programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almost-sure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almost-sure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on benchmarks adapted from previous work to demonstrate the effectiveness of our approach.