Dohan Kim
Logical Methods in Computer Science 2025.
pdfAbstract
his paper presents a new framework for constructing congruence closure of a finite set of ground equations over uninterpreted symbols and interpreted symbols for the group axioms. In this framework, ground equations are flattened into certain forms by introducing new constants, and a completion procedure is performed on ground flat equations. The proposed completion procedure uses equational inference rules and constructs a ground convergent rewrite system for congruence closure with such interpreted symbols. If the completion procedure terminates, then it yields a decision procedure for the word problem for a finite set of ground equations with respect to the group axioms. This paper also provides a sufficient terminating condition of the completion procedure for constructing a ground convergent rewrite system from ground flat equations containing interpreted symbols for the group axioms. In addition, this paper presents a new method for constructing congruence closure of a finite set of ground equations containing interpreted symbols for the semigroup, monoid, and the multiple disjoint sets of group axioms, respectively, using the proposed framework.
BibTex
@article{DBLP:journals/lmcs/Kim25, author = {Dohan Kim}, title = {Congruence Closure Modulo Groups}, journal = {Log. Methods Comput. Sci.}, volume = {21}, number = {1}, year = {2025}, url = {https://doi.org/10.46298/lmcs-21(1:20)2025}, doi = {10.46298/LMCS-21(1:20)2025}, timestamp = {Fri, 04 Apr 2025 16:39:05 +0200}, biburl = {https://dblp.org/rec/journals/lmcs/Kim25.bib}, bibsource = {dblp computer science bibliography, https://dblp.org}}