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Induction for Positive Almost Sure Termination

Isabelle Gnaedig 1 
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : In this paper, we propose an inductive approach to prove positive almost sure termination of probabilistic rewriting under the innermost strategy. We extend to the probabilistic case a technique we proposed for termination of usual rewriting under strategies. The induction principle consists in assuming that terms smaller than the starting terms for an induction ordering are positively almost surely terminating. The proof is developed in generating proof trees, modelizing rewriting trees, in alternatively applying abstraction steps, expressing the application of the induction hypothesis, and narrowing steps, simulating the possible rewriting steps after abstraction. This technique can be fully automatized, in particular for rewrite systems on constants, very useful to modelize probabilistic protocols.
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Submitted on : Wednesday, October 10, 2018 - 7:16:54 PM
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Isabelle Gnaedig. Induction for Positive Almost Sure Termination. PPDP 2007 - 9th ACM-SIGPLAN International Symposium on Principles and Practice of Declarative Programming, Jul 2007, Wroclaw, Poland. pp.167-177. ⟨inria-00182435⟩



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