Year: 2021
Type: article
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.
DOI: 10.4204/eptcs.342.8
Authors: Dohan Kim, Christopher Lynch
Institution: Clarkson University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W3198007607