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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Published in | Processes, Terms and Cycles: Steps on the Road to Infinity pp. 280 - 308 |
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Main Author | |
Format | Book Chapter |
Language | English |
Published |
Berlin, Heidelberg
Springer Berlin Heidelberg
2005
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Series | Lecture Notes in Computer Science |
Subjects | |
Online Access | Get full text |
ISBN | 354030911X 9783540309116 |
ISSN | 0302-9743 1611-3349 |
DOI | 10.1007/11601548_16 |
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Abstract | 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. |
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AbstractList | 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. |
Author | Plump, Detlef |
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Copyright | Springer-Verlag Berlin Heidelberg 2005 |
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DOI | 10.1007/11601548_16 |
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Editor | van Oostrom, Vincent van Raamsdonk, Femke de Vrijer, Roel Middeldorp, Aart |
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PublicationSubtitle | Essays Dedicated to Jan Willem Klop on the Occasion of His 60th Birthday |
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Snippet | 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... |
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Title | Confluence of Graph Transformation Revisited |
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