Generalized Eilenberg Theorem I: Local Varieties of Languages
Adámek J, Milius S, Myers R, Urbat H, Urbat H (2014)
Publication Type: Conference contribution
Publication year: 2014
Publisher: Springer
Edited Volumes: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Series: Lecture Notes Comput. Sci.
City/Town: Berlin/Heidelberg
Book Volume: 8412
Pages Range: 366-380
Conference Proceedings Title: Foundations of Software Science and Computation Structures
Event location: Grenoble, France
ISBN: 978-3-642-54830-7
URI: http://www.stefan-milius.eu
DOI: 10.1007/978-3-642-54830-7_24
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 Σ closed under derivatives is isomorphic to the lattice of all pseudovarieties of Σ-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 due to Polák weakens them to join-semilattices, and the last one considers vector spaces over ℤ
Authors with CRIS profile
Stefan Milius
Lehrstuhl für Informatik 8 (Theoretische Informatik)
Henning Urbat
Lehrstuhl für Informatik 8 (Theoretische Informatik)
Involved external institutions
Germany (DE)How to cite
APA:
Adámek, J., Milius, S., Myers, R., Urbat, H., & Urbat, H. (2014). Generalized Eilenberg Theorem I: Local Varieties of Languages. In Foundations of Software Science and Computation Structures (pp. 366-380). Grenoble, France, FR: Berlin/Heidelberg: Springer.
MLA:
Adámek, Jiří, et al. "Generalized Eilenberg Theorem I: Local Varieties of Languages." Proceedings of the FoSSaCS'14, Grenoble, France Berlin/Heidelberg: Springer, 2014. 366-380.
BibTeX: Download