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On n-syntactic equational theories

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Algebraic and Logic Programming (ALP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 632))

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Abstract

We define the n-syntactic theories as a natural extension of the syntactic theories. A n-syntactic theory is an equational theory which admits a finite presentation in which every proof can be performed with at most n applications of an axiom at the root, but no finite presentation in which every proof can be performed with at most n − 1 applications of an axiom at the root. The n-syntactic theories inherit the good properties of the syntactic theories for solving the word problem, or matching or unification problems. We show that for any integer n ≥ 1, there exists a n-syntactic theory.

This research was supported in part by GRECO Programmation CNRS and ESPRIT Working Group COMPASS.

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Authors and Affiliations

  1. Centre d'Orsay, LRI, CNRS URA 410 Université Paris-Sud, 91405, Orsay Cedex

    Alexandre Boudet & Evelyne Contejean

Authors
  1. Alexandre Boudet
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  2. Evelyne Contejean
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Editor information

Hélène Kirchner Giorgio Levi

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© 1992 Springer-Verlag Berlin Heidelberg

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Boudet, A., Contejean, E. (1992). On n-syntactic equational theories. In: Kirchner, H., Levi, G. (eds) Algebraic and Logic Programming. ALP 1992. Lecture Notes in Computer Science, vol 632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013843

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  • DOI: https://doi.org/10.1007/BFb0013843

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55873-6

  • Online ISBN: 978-3-540-47302-2

  • eBook Packages: Springer Book Archive

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