Abstract
In this paper we initiate the following program: Associate sets of finite words to Büchi-recognizable sets of infinite words, and reduce algorithmic problems on Büchi automata to simpler ones on automata on finite words. We know that the set of ultimately periodic words UP(L) of a rational language of infinite words L is sufficient to characterize L, since UP(L 1)=UP(L 2) implies L 1=L 2. We can use this fact as a test, for example, of the equivalence of two given Büchi automata. The main technical result in this paper is the construction of an automaton which recognizes the set of all finite words u · $ · v which naturally represent the ultimately periodic words of the form u · 554-01 in the language of infinite words recognized by a given Büchi automaton.
Preview
Unable to display preview. Download preview PDF.
Bibliography
Arnold, A., ”A Syntactic Congruence for Rational ω-Languages,” Theoretical Computer Science, 39, (1985), 333–335.
Calbrix, H., Nivat, M., Podelski, A., ”Une méthode de décision de la logique monadique du second ordre d'une fonction successeur”, submited to Comptes Rendus de l'Académie des Sciences, Série I.
Calbrix, H., Nivat, M., Podelski, A., ”Sur les mots ultimement périodiques des langages rationnels de mots infinis”, submited to Comptes Rendus de l'Académie des Sciences, Série I.
Eilenberg, S., ”Automata, Languages and Machines,” Vol. A, Academic Press, (1974).
Safra, S., ”On the complexity of ω-automata,” in: Proc. 29th Ann. IEEE Symp. on Foundations of Computer Science, (1988), 319–327.
Sistla, A.P., M.Y. Vardi and P. Volper, ”The Complementation Problem for Büchi automata with Application to Temporal Logic,” Theoret. Comput. Sci., 49, (1987), 217–237.
Thomas, W., ”Automata on Infinite Objects,” in Handbook of Theoretical Computer Science, J. van Leeuven ed., Elsevier, (1990), 133–191.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Calbrix, H., Nivat, M., Podelski, A. (1994). Ultimately periodic words of rational ω-languages. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1993. Lecture Notes in Computer Science, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58027-1_27
Download citation
DOI: https://doi.org/10.1007/3-540-58027-1_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58027-0
Online ISBN: 978-3-540-48419-6
eBook Packages: Springer Book Archive