Confluence of Layered Rewrite Systems
Logic in Computer Science
2015-09-16 v1
Abstract
We investigate the new, Turing-complete class of layered systems, whose lefthand sides of rules can only be overlapped at a multiset of disjoint or equal positions. Layered systems define a natural notion of rank for terms: the maximal number of non-overlapping redexes along a path from the root to a leaf. Overlappings are allowed in finite or infinite trees. Rules may be non-terminating, non-left-linear, or non-right-linear. Using a novel unification technique, cyclic unification, and the so-alled subrewriting relation, we show that rank non-increasing layered systems are confluent provided their cyclic critical pairs have cyclic-joinable decreasing diagrams.
Cite
@article{arxiv.1509.04699,
title = {Confluence of Layered Rewrite Systems},
author = {Jean-Pierre Jouannaud and Jiaxiang Liu and Mizuhito Ogawa},
journal= {arXiv preprint arXiv:1509.04699},
year = {2015}
}