Varieties
arXiv:1502.03951 · doi:10.4171/Automata
Abstract
This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages. In the introductory section, we present a number of examples that illustrate and motivate the fundamental concepts. We do this for the most part without proofs, and often without precise definitions, leaving these to the formal development of the theory that begins in Section 2. Our presentation of the theory draws heavily on the work of Gehrke, Grigorieff and Pin (2008) on the equational theory of lattices of regular languages. In the subsequent sections we consider in more detail aspects of varieties that were only briefly evoked in the introduction: Decidability, operations on languages, and characterizations in formal logic.
This is a chapter in an upcoming Handbook of Automata Theory
References in corpus (9)
- Amenability via random walks
- Thurston equivalence of topological polynomials
- L-presentations and branch groups
- Amenability of linear-activity automaton groups
- On the Word and Period Growth of some Groups of Tree Automorphisms
- Classification of groups generated by 3-state automata over a 2-letter alphabet
- The smallest Mealy automaton of intermediate growth
- Adding successor: A transfer theorem for separation and covering
- Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable