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Zbl 1088.68117
Ésik, Zoltán; Kuich, Werner
Equational axioms for a theory of automata. (English)
[A] Mart\'in-Vide, Carlos (ed.) et al., Formal languages and applications. Berlin: Springer. Studies in Fuzziness and Soft Computing 148, 183-196 (2004). ISBN 3-540-20907-7/hbk

Summary: A Conway semiring is a starsemiring that satisfies the sum-star-equation and the product-star-equation. Many results in the theory of automata and languages only depend on the equations defining Conway semirings. We introduce semirings, formal power series and matrices, define Conway semirings and state some of their important properties. Then we prove a Kleene Theorem in Conway semirings. Eventually, we discuss the computation of the star of a matrix with entries in a Conway semiring.

MSC 2000:: *68Q70 Algebraic theory of automata
16Y60 Semirings
68Q45 Formal languages

Keywords: Conway semiring; starsemiring

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