JUCS - Journal of Universal Computer Science 8(2): 173-183, doi: 10.3217/jucs-008-02-0173
Rationally Additive Semirings
expand article infoZoltán Ésik‡, Werner Kuich§
‡ Department of Computer Science, The University of Szeged, Szeged, Hungary§ Institut für Algebra und Computermathematik, Technische Universität Wien, Wien, Austria

Corresponding author: Zoltán Ésik ( esik@inf.u-szeged.hu )

© Zoltán Ésik, Werner Kuich.
This article is freely available under the J.UCS Open Content License.
Citation: Ésik Z, Kuich W (2002) Rationally Additive Semirings. JUCS - Journal of Universal Computer Science 8(2): 173-183. https://doi.org/10.3217/jucs-008-02-0173
Open Access
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
semiring, complete semiring, iteration semiring, fixed point, power series