Generalized Eilenberg Theorem I: Local Varieties of Languages
Author(s): Adámek J, Milius S, Myers R, Urbat H
Title edited volumes: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publishing place: Berlin/Heidelberg
Publication year: 2014
Title of series: Lecture Notes Comput. Sci.
Conference Proceedings Title: Foundations of Software Science and Computation Structures
Pages range: 366-380
Event location: Grenoble, France
Start date of the event: 05/04/2014
End date of the event: 13/04/2014
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 ℤ2. © 2014 Springer-Verlag.
FAU Authors / FAU Editors How to cite
APA: Adámek, J., Milius, S., Myers, R., & Urbat, H. (2014). Generalized Eilenberg Theorem I: Local Varieties of Languages. In Foundations of Software Science and Computation Structures (pp. 366-380). 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.