Termination of cycle rewriting by transformation and matrix interpretation

  • We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and then apply state of the art techniques to prove termination of the string rewrite system. We present three such transformations, and prove for all of them that they are sound and complete. In this way not only termination of string rewriting of the transformed system implies termination of the original cycle rewrite system, a similar conclusion can be drawn for non-termination. Apart from this transformational approach, we present a uniform framework of matrix interpretations, covering most of the earlier approaches to automatically proving termination of cycle rewriting. All our techniques serve both for proving termination and relative termination. We present several experiments showing the power of our techniques.

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Author:David SabelORCiDGND, Hans Zantema
ArXiv Id:http://arxiv.org/abs/1609.07065
Document Type:Report
Date of Publication (online):2016/12/21
Date of first Publication:2016/09/22
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2016/12/21
Tag:relative termination; rewriting systems; string rewriting; termination
Page Number:38
(c) D. Sabel and H. Zantema Creative Commons
Institutes:Informatik und Mathematik / Informatik
CCS-Classification:F. Theory of Computation / F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES / F.4.2 Grammars and Other Rewriting Systems (D.3.1)
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoCreative Commons - Namensnennung 4.0