Eilenberg's variety theorem without Boolean operations

Birkmann F, Milius S, Urbat H (2022)

Publication Type: Journal article

Publication year: 2022


Article Number: 104916

DOI: 10.1016/j.ic.2022.104916


Eilenberg's variety theorem marked a milestone in the algebraic theory of regular languages by establishing a formal correspondence between properties of regular languages and properties of finite monoids recognizing them. Motivated by classes of languages accepted by quantum finite automata, we introduce basic varieties of regular languages, a weakening of Eilenberg's original concept that does not require closure under any boolean operations, and prove a variety theorem for them. To do so, we investigate the algebraic recognition of languages by lattice bimodules, generalizing Klíma and Polák's lattice algebras, and we utilize the duality between algebraic completely distributive lattices and posets.

Authors with CRIS profile

How to cite


Birkmann, F., Milius, S., & Urbat, H. (2022). Eilenberg's variety theorem without Boolean operations. Information and Computation. https://dx.doi.org/10.1016/j.ic.2022.104916


Birkmann, Fabian, Stefan Milius, and Henning Urbat. "Eilenberg's variety theorem without Boolean operations." Information and Computation (2022).

BibTeX: Download