Generalized Eilenberg Theorem I: Local Varieties of Languages
Formal Languages and Automata Theory
2015-01-19 v1 Logic in Computer Science
Category Theory
Abstract
We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages over an alphabet {\Sigma} closed under derivatives is isomorphic to the lattice of all pseudovarieties of {\Sigma}-generated monoids. By applying our method to different categories, we obtain three related results: one, due to Gehrke, Grigorieff and Pin, weakens boolean algebras to distributive lattices, one weakens them to join-semilattices, and the last one considers vector spaces over the binary field.
Cite
@article{arxiv.1501.02834,
title = {Generalized Eilenberg Theorem I: Local Varieties of Languages},
author = {Jiri Adamek and Stefan Milius and Robert Myers and Henning Urbat},
journal= {arXiv preprint arXiv:1501.02834},
year = {2015}
}