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International Conference on Rewriting Techniques and Applications

RTA 2005: Term Rewriting and Applications pp 453–468Cite as

Proof-Producing Congruence Closure

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 3467)

Abstract

Many applications of congruence closure nowadays require the ability of recovering, among the thousands of input equations, the small subset that caused the equivalence of a given pair of terms. For this purpose, here we introduce an incremental congruence closure algorithm that has an additional \(\mathit{Explain}\) operation.

First, two variations of union-find data structures with \(\mathit{Explain}\) are introduced. Then, these are applied inside a congruence closure algorithm with \(\mathit{Explain}\), where a k-step proof can be recovered in almost optimal time (quasi-linear in k), without increasing the overall O(n log n) runtime of the fastest known congruence closure algorithms.

This non-trivial (ground) equational reasoning result has been quite intensively sought after (see, e.g., [SD99,dMRS04,KS04]), and moreover has important applications to verification.

Keywords

  • Decision Procedure
  • Recursive Call
  • Congruence Relation
  • Proof Tree
  • Union Operation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-540-32033-3_33
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Authors and Affiliations

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

    Robert Nieuwenhuis & Albert Oliveras

Authors
  1. Robert Nieuwenhuis
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  2. Albert Oliveras
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Editor information

Editors and Affiliations

  1. LuFG Informatik 2, RWTH Aachen University, Germany

    Jürgen Giesl

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Nieuwenhuis, R., Oliveras, A. (2005). Proof-Producing Congruence Closure. In: Giesl, J. (eds) Term Rewriting and Applications. RTA 2005. Lecture Notes in Computer Science, vol 3467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32033-3_33

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  • DOI: https://doi.org/10.1007/978-3-540-32033-3_33

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