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International Workshop on Word Equations and Related Topics

IWWERT 1991: Word Equations and Related Topics pp 150–176Cite as

Word unification and transformation of generalized equations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 677))

Abstract

Makanin's algorithm [Ma77] shows that it is decidable whether a word equation has a solution. The original description was hard to understand and not designed for implementation. Since words represent a fundamental data type, various authors have given improved descriptions [Pé81, Ab87, Sc90, Ja90]. In this paper we present a version of the algorithm which probably cannot be further simplified without fundamentally new insights which exceed Makanin's original ideas. We give a transformation rule which is efficient, conceptually simple and applies to arbitrary generalized equations. No further subprocedure is needed for search tree generation. In contrast to our older work in [Sc90] the presentation will be based on Jaffar's [Ja90] notion of generalized equations. We also prove that a combination of Plotkin's algorithm (see [P172], also [Le72]) and Makanin's algorithm offers a simple solution to the problem of terminating minimal and complete word unification.

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Authors and Affiliations

  1. Centrum für Informations- und Sprachverarbeituug (CIS), University Munich, Leopoldstr. 139, D-8000, Munich 40

    Klaus U. Schulz

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  1. Klaus U. Schulz
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Habib Abdulrab Jean-Pierre Pécuchet

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© 1993 Springer-Verlag Berlin Heidelberg

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Schulz, K.U. (1993). Word unification and transformation of generalized equations. In: Abdulrab, H., Pécuchet, JP. (eds) Word Equations and Related Topics. IWWERT 1991. Lecture Notes in Computer Science, vol 677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56730-5_36

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  • DOI: https://doi.org/10.1007/3-540-56730-5_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56730-1

  • Online ISBN: 978-3-540-47636-8

  • eBook Packages: Springer Book Archive

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