An algebraic approach to hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Automata, Languages, and Machines
Automata, Languages, and Machines
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Myhill--Nerode type theory for fuzzy languages and automata
Fuzzy Sets and Systems
Myhill-Nerode theorem for sequential transducers over unique GCD-Monoids
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
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The Myhill-Nerode Theorem states that the equivalence relation ~"L given by a language L has finite index if and only if L is accepted by a finite automaton. In this paper we give several generalizations of the theorem which are algebraic in nature. In our versions, a finiteness condition involving the action of a semigroup on a certain function plays the role of the finiteness of the index of ~"L, while various algebraic structures including algebras, coalgebras, and bialgebras play the role of the finite automaton which accepts the language. We develop additional theory concerning the algebraic objects which so arise, and study the minimal ones.