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Normal Forms and Reduction for Theories of Binary Relations

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Rewriting Techniques and Applications (RTA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1833))

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Abstract

We consider equational theories of binary relations, in a language expressing composition, converse, and lattice operations. We treat the equations valid in the standard model of sets and also define a hierarchy of equational axiomatisations stratifying the standard theory. By working directly with a presentation of relation-expressions as graphs we are able to define a notion of reduction which is confluent and strongly normalising, in sharp contrast to traditional treatments based on first-order terms. As consequences we obtain unique normal forms, decidability of the decision problem for equality for each theory. In particular we show a non-deterministic polynomial-time upper bound for the complexity of the decision problems.

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Author information

Authors and Affiliations

  1. Computer Science Group, Wesleyan University, Middletown, CT, 06459, USA

    Dan Dougherty & Claudio Gutiérrez

Authors
  1. Dan Dougherty
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  2. Claudio Gutiérrez
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Stony Brook University, Stony Brook, P.O. Box, New York

    Leo Bachmair

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© 2000 Springer-Verlag Berlin Heidelberg

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Dougherty, D., Gutiérrez, C. (2000). Normal Forms and Reduction for Theories of Binary Relations. In: Bachmair, L. (eds) Rewriting Techniques and Applications. RTA 2000. Lecture Notes in Computer Science, vol 1833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721975_7

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  • DOI: https://doi.org/10.1007/10721975_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67778-9

  • Online ISBN: 978-3-540-44980-5

  • eBook Packages: Springer Book Archive

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