Confluence of Graph Transformation Revisited

It is shown that it is undecidable in general whether a terminating graph rewriting system is confluent or not—in contrast to the situation for term and string rewriting systems. Critical pairs are introduced to hypergraph rewriting, a generalisation of graph rewriting, where it turns out that the m...

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Bibliographic Details
Published inProcesses, Terms and Cycles: Steps on the Road to Infinity pp. 280 - 308
Main Author Plump, Detlef
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
SeriesLecture Notes in Computer Science
Subjects
Critical Pair
Direct Derivation
Graph Grammar
Graph Transformation
Rule Schema
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ISBN354030911X
9783540309116
ISSN0302-9743
1611-3349
DOI10.1007/11601548_16

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Summary:It is shown that it is undecidable in general whether a terminating graph rewriting system is confluent or not—in contrast to the situation for term and string rewriting systems. Critical pairs are introduced to hypergraph rewriting, a generalisation of graph rewriting, where it turns out that the mere existence of common reducts for all critical pairs of a graph rewriting system does not imply local confluence. A Critical Pair Lemma for hypergraph rewriting is then established which guarantees local confluence if each critical pair of a system has joining derivations that are compatible in that they map certain nodes to the same nodes in the common reduct.
ISBN:354030911X
9783540309116
ISSN:0302-9743
1611-3349
DOI:10.1007/11601548_16