Proving Positive Almost-Sure Termination

Olivier Bournez 1 Florent Garnier 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In order to extend the modeling capabilities of rewriting systems, it is rather natural to consider that the firing of rules can be subject to some probabilistic laws. Considering rewrite rules subject to probabilities leads to numerous questions about the underlying notions and results. We focus here on the problem of termination of a set of probabilistic rewrite rules. A probabilistic rewrite system is said almost surely terminating if the probability that a derivation leads to a normal form is one. Such a system is said positively almost surely terminating if furthermore the mean length of a derivation is finite. We provide several results and techniques in order to prove positive almost sure termination of a given set of probabilistic rewrite rules. All these techniques subsume classical ones for non-probabilistic systems.
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[Intern report] A04-R-409 || bournez04h, 2004, 16 p
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https://hal.inria.fr/inria-00099867
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Soumis le : mardi 26 septembre 2006 - 09:56:46
Dernière modification le : jeudi 11 janvier 2018 - 06:19:59
Document(s) archivé(s) le : vendredi 25 novembre 2016 - 12:20:19

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Olivier Bournez, Florent Garnier. Proving Positive Almost-Sure Termination. [Intern report] A04-R-409 || bournez04h, 2004, 16 p. 〈inria-00099867〉

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