Varieties of Data Languages
Abstract
We establish an Eilenberg-type correspondence for data languages, i.e. languages over an infinite alphabet. More precisely, we prove that there is a bijective correspondence between varieties of languages recognized by orbit-finite nominal monoids and pseudovarieties of such monoids. This is the first result of this kind for data languages. Our approach makes use of nominal Stone duality and a recent category theoretic generalization of Birkhoff-type HSP theorems that we instantiate here for the category of nominal sets. In addition, we prove an axiomatic characterization of weak pseudovarieties as those classes of orbit-finite monoids that can be specified by sequences of nominal equations, which provides a nominal version of a classical theorem of Eilenberg and Sch\"utzenberger.
Cite
@article{arxiv.1903.08053,
title = {Varieties of Data Languages},
author = {Henning Urbat and Stefan Milius},
journal= {arXiv preprint arXiv:1903.08053},
year = {2019}
}