Finding and Certifying Loops

Authors:
Harald Zankl;Christian Sternagel;Dieter Hofbauer;Aart Middeldorp
Affiliations:
University of Innsbruck, Innsbruck, Austria;University of Innsbruck, Innsbruck, Austria;Berufsakademie Nordhessen, Bad Wildungen, Germany;University of Innsbruck, Innsbruck, Austria
Venue:
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Year:
2009

Citing 18
Cited 1

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Proving non-looping non-termination automatically

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Abstract

The first part of this paper presents a new approach for automatically proving nontermination of string rewrite systems. We encode rewrite sequences as propositional formulas such that a loop can be extracted from a satisfying assignment. Alternatively, loops can be found by enumerating forward closures. In the second part we give a formalization of loops in the theorem prover Isabelle/HOL. Afterwards, we use Isabelle's code-generation facilities to certify loops. The integration of our approach in CeTA (a program for automatic certification of termination proofs) makes it the first tool capable of certifying nontermination.