| A Geometric Proof of Confluence by Decreasing Diagrams (2007) | |||||||||||||||||
Abstract | |||||||||||||||||
| Recently a new confluence criterion for confluence was found using decreasing diagrams, as a generalization of several wellknown confluence criteria in abstract rewriting such as the strong confluence lemma. We give a new proof of the decreasing diagram theorem based on a geometric study of infinite reduction diagrams, arising from unsuccesful attempts to obtain a confluent diagram by tiling with elementary diagrams. Contents 1. Introduction 2. Abstract Reduction Systems 3. Finite reduction diagrams 4. Infinite reduction diagrams and towers 5. Tree coverings of reduction diagrams 6. Impossible tree coverings 7. Confluence by decreasing diagrams 8. References 2 1. Introduction Abstract rewriting is the initial part of the theory of rewriting where objects have no structure and the rewrite relation is just a binary relation on the set of objects. Usually there is not one but an indexed family of rewrite relations present. There are several useful and well-known lemma's for such abstr... | |||||||||||||||||
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