A Survey on the Local Divisor Technique
Formal Languages and Automata Theory
2023-03-17 v4 Logic in Computer Science
Abstract
Local divisors allow a powerful induction scheme on the size of a monoid. We survey this technique by giving several examples of this proof method. These applications include linear temporal logic, rational expressions with Kleene stars restricted to prefix codes with bounded synchronization delay, Church-Rosser congruential languages, and Simon's Factorization Forest Theorem. We also introduce the notion of localizable language class as a new abstract concept which unifies some of the proofs for the results above. The current arXiv-version includes some additional material about codes of bounded synchronization delay as well as some updates concerning related literature.
Keywords
Cite
@article{arxiv.1410.6026,
title = {A Survey on the Local Divisor Technique},
author = {Volker Diekert and Manfred Kufleitner},
journal= {arXiv preprint arXiv:1410.6026},
year = {2023}
}
Comments
20 pages,