eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-07-04
130:1
130:14
10.4230/LIPIcs.ICALP.2019.130
article
Varieties of Data Languages (Track B: Automata, Logic, Semantics, and Theory of Programming)
Urbat, Henning
1
Milius, Stefan
1
Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
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 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 Schützenberger.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol132-icalp2019/LIPIcs.ICALP.2019.130/LIPIcs.ICALP.2019.130.pdf
Nominal sets
Stone duality
Algebraic language theory
Data languages