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Volume 8 / Issue 2

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DOI:   10.3217/jucs-008-02-0173


Rationally Additive Semirings

Zoltán Ésik (Department of Computer Science, The University of Szeged, Hungary)

Werner Kuich (Institut für Algebra und Computermathematik, Technische Universität Wien, Austria)

Abstract: We define rationally additive semirings that are a generalization of (ω)-complete and (ω)-continuous semirings. We prove that every rationally additive semiring is an iteration semiring. Moreover, we characterize the semirings of rational power series with coefficients in , the semiring of natural numbers equipped with a top element, as the free rationally additive semirings

1.) C. S. Calude, K. Salomaa, S. Yu (eds.). Advances and Trends in Automata and Formal Languages. A Collection of Papers in Honour of the 60th Birthday of Helmut Jürgensen.

Keywords: complete semiring, fixed point, iteration semiring, power series, semiring

Categories: F.4.3