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Proving Positive Almost-Sure Termination

  • Olivier Bournez
  • Florent Garnier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3467)

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.

Keywords

Markov Chain Function Versus Markov Decision Process Realizable History Homogeneous Markov Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Olivier Bournez
    • 1
  • Florent Garnier
    • 1
  1. 1.LORIA/INRIAVillers lès Nancy CedexFrance

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