A Data Structure to Handle Large Sets of Equal Terms

14 pages•Published: March 27, 2016

Baudouin Le Charlier and Mêton Mêton Atindehou

Abstract

We present a data structure to represent and manipulate large sets of (equal) terms (or expressions). Our initial and main motivation for this data structure is the simplification of expressions with respect to a formal theory, typically, an equational one. However, it happens that the data structure is also efficient to compute the congruence closure of a relation over a set of terms.
We provide an abstract definition of the data structure, including a precise semantics, and we explain how to implement it efficiently. We prove the correctness of the proposed algorithms, with a complexity analysis and experimental results. We compare these algorithms with previous algorithms to compute the congruence closure and we also sketch how we use the data structure to tackle the expression simplification problem.

Keyphrases: congruence closure, data structure, decision procedure, expression simplification, term equivalence, theory of equality

In: James H. Davenport and Fadoua Ghourabi (editors). SCSS 2016. 7th International Symposium on Symbolic Computation in Software Science, vol 39, pages 81-94.

Links:	https://easychair.org/publications/paper/5Wj
	https://doi.org/10.29007/hsbm

BibTeX entry

@inproceedings{SCSS2016:Data_Structure_Handle_Large,
  author    = {Baudouin Le Charlier and Mêton Mêton Atindehou},
  title     = {A Data Structure to Handle Large Sets of Equal Terms},
  booktitle = {SCSS 2016. 7th International Symposium on  Symbolic Computation in Software Science},
  editor    = {James H. Davenport and Fadoua Ghourabi},
  series    = {EPiC Series in Computing},
  volume    = {39},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/5Wj},
  doi       = {10.29007/hsbm},
  pages     = {81-94},
  year      = {2016}}

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