English

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.

Keywords

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}
}
R2 v1 2026-06-22T10:57:34.075Z