Abstract
This paper continues the algebraic theory of Ésik, Kuich [9] on semiring-semimodule pairs and quemirings that is applicable to languages that contain finite and infinite words. The main advantage is that we get rid of the idempotency assumption for the semimodule needed at several places in Ésik, Kuich [9].
Additionally, we consider linear systems as a generalization of rightlinear grammars. Moreover, we develop an algorithm that constructs, for a given finite automaton, an equivalent one without ε-moves.
Partially supported by Aktion Österreich-Ungarn, Wissenschafts- und Erziehungskooperation, Projekt 53ÖU1.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bloom, S.L., Ésik, Z.: Iteration Theories. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1993)
Bouyer, P., Petit, A.: A Kleene/Büchi-like theorem for clock languages. J. of Automata, Languages and Combinatorics 7, 167–186 (2002)
Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Proc. Int. Congr. Logic, Methodology and Philosophy of Science, 1960, pp. 1–11. Stanford University Press (1962)
Conway, J.H.: Regular Algebra and Finite Machines. Chapman & Hall, Boca Raton (1971)
Droste, M., Kuske, D.: Skew and infinitary formal power series. Technical Report 2002–38, Department of Mathematics and Computer Science, University of Leicester
Elgot, C.: Matricial theories. J. Algebra 42, 391–422 (1976)
Ésik, Z., Kuich, W.: Inductive ∗-semirings. To appear in Theoretical Computer Science
Ésik, Z., Kuich, W.: On iteration semiring-semimodule pairs (to appear)
Ésik, Z., Kuich, W.: A semiring-semimodule generalization of ω-regular languages I. Technical Report, Technische Universität Wien (2003)
Ésik, Z., Kuich, W.: A semiring-semimodule generalization of ω-regular languages II. Technical Report, Technische Universität Wien (2003)
Kuich, W., Salomaa, A.: Semirings, Automata, Languages. EATCS Monographs on Theoretical Computer Science, vol. 5. Springer, Heidelberg (1986)
Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)
Perrin, D., Pin, J.-E.: Infinite Words. Elsevier, Amsterdam (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ésik, Z., Kuich, W. (2004). An Algebraic Generalization of ω-Regular Languages. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_50
Download citation
DOI: https://doi.org/10.1007/978-3-540-28629-5_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22823-3
Online ISBN: 978-3-540-28629-5
eBook Packages: Springer Book Archive