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Equational axioms for a theory of automata. (English) Zbl 1088.68117
Martín-Vide, Carlos (ed.) et al., Formal languages and applications. Berlin: Springer (ISBN 3-540-20907-7/hbk). Studies in Fuzziness and Soft Computing 148, 183-196 (2004).
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. For the entire collection see [Zbl 1051.68020].
68Q70Algebraic theory of languages and automata
68Q45Formal languages and automata