Abstract
A Conway semiring is a semiring S equipped with a unary operation *:S → S, called “star”, satisfying the sum star and product star identities. A Conway semiring-semimodule pair consists of a Conway semiring S and a left S-semimodule V together with a function ω: S → V, called “omega power”, subject to the sum omega and product omega identities. A Kleene type theorem holds in all Conway semiring-semimodule pairs that can be instantiated to give the equivalence of Büchi automata and regular languages over ω-words. However, sometimes the star and omega power operations cannot be defined in an appropriate manner on the whole semiring S. To handle this situation, we introduce partial Conway semiring-semimodule pairs and develop their basic theory in connection with automata. We prove a Kleene theorem, applicable to all partial Conway semiring-semimodule pairs.
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Ésik, Z. (2011). Partial Conway and Iteration Semiring-Semimodule Pairs. In: Kuich, W., Rahonis, G. (eds) Algebraic Foundations in Computer Science. Lecture Notes in Computer Science, vol 7020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24897-9_3
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DOI: https://doi.org/10.1007/978-3-642-24897-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24896-2
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