Distributed Coalgebraic Partition Refinement - Birkmann, Fabian; Deifel, Hans-Peter; Milius, Stefan (TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS, TACAS 2022, PT II, 2022)
CRIS-Team WoS Importer:2022-04-29

Eilenberg's variety theorem without Boolean operations - Birkmann, Fabian; Milius, Stefan; Urbat, Henning (Information and Computation, 2022)
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.
CRIS-Team Scopus Importer:2022-05-20
Keywords: Eilenberg's theorem; Pseudovariety; Quantum finite automata; Variety of regular languages

On Language Varieties Without Boolean Operations - Birkmann, Fabian; Milius, Stefan; Urbat, Henning (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2021)
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.
CRIS-Team Scopus Importer:2021-04-30