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Critical pairs in term graph rewriting

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Mathematical Foundations of Computer Science 1994 (MFCS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 841))

Abstract

Term graphs represent functional expressions such that common subexpressions can be shared, making expression evaluation more efficient than with strings or trees. Rewriting of term graphs proceeds by both applications of term rewrite rules and folding steps which enhance the degree of sharing. The present paper introduces critical pairs in term graph rewriting and establishes a Critical Pair Lemma as an analogue to the well-known result in term rewriting. This leads to a decision procedure for confluence in the presence of termination. As a by-product, the procedure can be used as a confluence test for term rewriting and as such it extends the classical test of Knuth and Bendix because it applies to all terminating and to certain non-terminating term rewriting systems.

Research partially supported by ESPRIT Basic Research Working Group 6112, COMPASS.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Universität Bremen, Postfach 33 04 40, 28334, Bremen, Germany

    Detlef Plump

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  1. Detlef Plump
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Igor Prívara Branislav Rovan Peter Ruzička

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© 1994 Springer-Verlag Berlin Heidelberg

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Plump, D. (1994). Critical pairs in term graph rewriting. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_102

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  • DOI: https://doi.org/10.1007/3-540-58338-6_102

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58338-7

  • Online ISBN: 978-3-540-48663-3

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