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Complexity of Linear Standard Theories

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2250))

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Abstract

We give an algorithm for deciding E-unification problems for linear standard equational theories (linear equations with all shared variables at a depth less than two) and varity 1 goals (linear equations with no shared variables). We show that the algorithm halts in quadratic time for the non-uniform E-unification problem, and linear time if the equational theory is varity 1. The algorithm is still polynomial for the uniform problem. The size of the complete set of unifiers is exponential, but membership in that set can be determined in polynomial time. For any goal (not just varity 1) we give a NEXPTIME algorithm.

This work was supported by NSF grant number CCR-9712388 and ONR grant number N00014-01-1-0435..

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Author information

Authors and Affiliations

  1. nDepartment of Mathematics and Computer Science Box 5815, Clarkson University, 13699-5815, Pscotsdam, NY, USA

    Barbara Morawska

Authors
  1. 1Christopher Lynch
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  2. Barbara Morawska
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Editor information

Editors and Affiliations

  1. Department of Software, Technical University of Catalonia, Jordi Girona 1, 08034, Barcelona, Spain

    Robert Nieuwenhuis

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

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Lynch, 1., Morawska, B. (2001). Complexity of Linear Standard Theories. In: Nieuwenhuis, R., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2001. Lecture Notes in Computer Science(), vol 2250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45653-8_13

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  • DOI: https://doi.org/10.1007/3-540-45653-8_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42957-9

  • Online ISBN: 978-3-540-45653-7

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