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Author (up) Intrigila, Benedetto; Salvo, Ivano; Sorgi, Stefano pdf  doi
  Title A characterization of weakly Church-Rosser abstract reduction systems that are not Church-Rosser Type Journal Article
  Year 2001 Publication Information and Computation Abbreviated Journal  
  Volume 171 Issue 2 Pages 137-155  
  Abstract Basic properties of rewriting systems can be stated in the framework of abstract reduction systems (ARS). Properties like confluence (or Church-Rosser, CR) and weak confluence (or weak Church-Rosser, WCR) and their relationships can be studied in this setting: as a matter of fact, well-known counterexamples to the implication WCR CR have been formulated as ARS. In this paper, starting from the observation that such counterexamples are structurally similar, we set out a graph-theoretic characterization of WCR ARS that is not CR in terms of a suitable class of reduction graphs, such that in every WCR not CR ARS, we can embed at least one element of this class. Moreover, we give a tighter characterization for a restricted class of ARS enjoying a suitable regularity condition. Finally, as a consequence of our approach, we prove some interesting results about ARS using the mathematical tools developed. In particular, we prove an extension of the Newmanââ¬â¢s lemma and we find out conditions that, once assumed together with WCR property, ensure the unique normal form property. The Appendix treats two interesting examples, both generated by graph-rewriting rules, with specific combinatorial properties.  
  Corporate Author Thesis  
  Publisher Academic Press, Inc. Place of Publication Duluth, MN, USA Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0890-5401 ISBN Medium  
  Area Expedition Conference  
  Notes Approved yes  
  Call Number Sapienza @ mari @ Intrigila-Salvo-Sorgi:01 Serial 68  
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