Ground Associative and Commutative Completion Modulo Shostak Theories

Sylvain Conchon; Evelyne Contejean; Mohamed Iguernelala

doi:10.29007/s69q

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Ground Associative and Commutative Completion Modulo Shostak Theories

6 pages•Published: March 25, 2013

Sylvain Conchon, Évelyne Contejean and Mohamed Iguernlala

Abstract

AC-completion efficiently handles equality modulo associative and commutative function symbols. In the ground case, the procedure terminates and provides a decision algorithm for the word problem. In this paper, we present a modular extension of ground AC-completion for deciding formulas in the combination of the theory of equality with user-defined AC symbols, uninterpreted symbols and an arbitrary signature disjoint Shostak theory X. The main ideas of our algorithm are first to adapt the definition of rewriting in order to integrate the canonizer of X and second, to replace the equation orientation mechanism found in ground AC-completion with the solver for X.

Keyphrases: AC-completion, associativity and commutativity, decision procedure, Shostak theories, SMT solvers

In: Andrei Voronkov, Geoff Sutcliffe, Matthias Baaz and Christian Fermüller (editors). LPAR-17-short. short papers for 17th International Conference on Logic for Programming, Artificial intelligence, and Reasoning., vol 13, pages 35--40

Links:	https://easychair.org/publications/paper/pzv
	https://doi.org/10.29007/s69q

BibTeX entry

@inproceedings{LPAR-17-short:Ground_Associative_and_Commutative,
  author    = {Sylvain Conchon and Evelyne Contejean and Mohamed Iguernelala},
  title     = {Ground Associative and Commutative Completion Modulo Shostak Theories},
  booktitle = {LPAR-17-short. short papers for 17th International Conference on Logic for Programming, Artificial intelligence, and Reasoning.},
  editor    = {Andrei Voronkov and Geoff Sutcliffe and Matthias Baaz and Christian Ferm\textbackslash{}"uller},
  series    = {EPiC Series in Computing},
  volume    = {13},
  pages     = {35--40},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/pzv},
  doi       = {10.29007/s69q}}

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