Eilenberg Theorems for Free [article]

Henning Urbat, Jiří Adámek, Liang-Ting Chen, Stefan Milius
2017 arXiv   pre-print
Eilenberg-type correspondences, relating varieties of languages (e.g. of finite words, infinite words, or trees) to pseudovarieties of finite algebras, form the backbone of algebraic language theory. Numerous such correspondences are known in the literature. We demonstrate that they all arise from the same recipe: one models languages and the algebras recognizing them by monads on an algebraic category, and applies a Stone-type duality. Our main contribution is a variety theorem that covers
more » ... Wilke's and Pin's work on ∞-languages, the variety theorem for cost functions of Daviaud, Kuperberg, and Pin, and unifies the two previous categorical approaches of Bojańczyk and of Adámek et al. In addition we derive a number of new results, including an extension of the local variety theorem of Gehrke, Grigorieff, and Pin from finite to infinite words.
arXiv:1602.05831v3 fatcat:rkuqhflgobfnhihwkauoolx5rm