Congruence Closure Modulo Permutation Equations
Abstract
We present a framework for constructing congruence closure modulo permutation equations, which extends the abstract congruence closure framework for handling permutation function symbols. Our framework also handles certain interpreted function symbols satisfying each of the following properties: idempotency (I), nilpotency (N), unit (U), I U U, or N U U. Moreover, it yields convergent rewrite systems corresponding to ground equations containing permutation function symbols. We show that congruence closure modulo a given finite set of permutation equations can be constructed in polynomial time using equational inference rules, allowing us to provide a polynomial time decision procedure for the word problem for a finite set of ground equations with a fixed set of permutation function symbols.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.03720
 Bibcode:
 2021arXiv210903720K
 Keywords:

 Computer Science  Logic in Computer Science
 EPrint:
 In Proceedings SCSS 2021, arXiv:2109.02501