Abstract
We consider partial Conway semirings and partial iteration semirings, both introduced by Bloom, Ésik, Kuich [2]. We develop a theory of cycle-free elements in partial iterative semirings that allows us to define cycle-free finite automata in partial iterative semirings and to prove a Kleene Theorem. We apply these results to power series over a graded monoid with discounting.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bloom, S.L., Ésik, Z.: Iteration Theories: The Equational Logic of Iterative Processes. EATCS monographs on Theoretical Computer Science. Springer, Heidelberg (1993)
Bloom, S.L., Ésik, Z., Kuich, W.: Partial Conway and iteration semirings. Fundamenta Informaticae 86, 19–40 (2008)
Conway, J.H.: Regular Algebra and Finite Machines. Chapman and Hall, Boca Raton (1971)
Droste, M., Kuich, W.: Semirings and formal power series. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata. EATCS Monographs on Theoretical Computer Science, ch. 1. Springer, Heidelberg (to appear, 2009)
Droste, M., Kuske, D.: Skew and infinitary formal power series. Theoretical Computer Science 366, 199–227 (2006)
Droste, M., Sakarovitch, J., Vogler, H.: Weighted automata with discounting. Information Processing Letters 108, 23–28 (2008)
Esik, Z., Kuich, W.: Equational axioms for a theory of automata. In: Martin-Vide, C., Mitrana, V., Paun, G. (eds.) Formal Languages and Applications. Studies in Fuzziness and Soft Computing, 148, pp. 183–196. Springer, Heidelberg (2004)
Esik, Z., Kuich, W.: Modern Automata Theory (2007), www.dmg.tuwien.ac.at/kuich
Ésik, Z., Kuich, W.: Finite Automata. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, ch. 3. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (to appear, 2009)
Kuich, W.: Kleene Theorems for skew formal power series. Acta Cybernetica 17, 719–749 (2006)
Kuich, W., Salomaa, A.: Semirings, Automata, Languages. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1986)
Sakarovitch, J.: Éléments de théorie des automates. Vuibert (2003)
Sakarovitch, J.: Rational and recognizable power series. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata. EATCS Monographs on Theoretical Computer Science, ch. 4. Springer, Heidelberg (to appear, 2009)
Schützenberger, M.P.: On the definition of a family of automata. Inf. Control 4, 245–270 (1961)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bloom, S.L., Ésik, Z., Kuich, W. (2009). Cycle-Free Finite Automata in Partial Iterative Semirings. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2009. Lecture Notes in Computer Science, vol 5725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03564-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-03564-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03563-0
Online ISBN: 978-3-642-03564-7
eBook Packages: Computer ScienceComputer Science (R0)