Regular Varieties of Automata and Coequations
نویسندگان
چکیده
In this paper we use a duality result between equations and coequations for automata, proved by Ballester-Bolinches, Cosme-Llópez, and Rutten to characterize nonempty classes of deterministic automata that are closed under products, subautomata, homomorphic images, and sums. One characterization is as classes of automata defined by regular equations and the second one is as classes of automata satisfying sets of coequations called varieties of languages. We show how our results are related to Birkhoff’s theorem for regular varieties.
منابع مشابه
The dual equivalence of equations and coequations for automata
Because of the isomorphism (X × A) → X ∼= X → X, the transition structure α : X → X of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. Here we will use this algebra-coalgebra duality of automata as a common perspective for the study of equations and coequations. Equations are sets of pairs of words (v, w) that ar...
متن کاملVarieties and Covarieties of Languages (Extended Abstract)
Because of the isomorphism (X × A) → X ∼= X → (A → X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebra-coalgebra duality goes back to Arbib and Manes, who formulated it as a duality between reachability and observability, and is ultimately based on Kalman’s duality in syst...
متن کاملVarieties and covarieties of languages ( preliminary version )
Because of the isomorphism (X × A) → X ∼= X → (A → X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebra-coalgebra duality goes back to Arbib and Manes, who formulated it as a duality between reachability and observability, and is ultimately based on Kalman’s duality in syst...
متن کاملEquations and Coequations for Weighted Automata
We study weighted automata from both an algebraic and a coalgebraic perspective. In particular, we consider equations and coequations for weighted automata. We prove a duality result that relates sets of equations (congruences) with (certain) subsets of coequations. As a consequence, we obtain two equivalent but complementary ways to define classes of weighted automata. We show that this dualit...
متن کاملOn Varieties of Automata Enriched with an Algebraic Structure (Extended Abstract)
Eilenberg correspondence, based on the concept of syntactic monoids, relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence related more general classes of regular languages with classes of more complex algebraic objects. Such generalized varieties also have natural counterparts formed by classes of finite automata equipped wi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015