Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T02:24:10.916Z Has data issue: false hasContentIssue false
  • English
  • Français

Computing the Rabin Index of a Parity Automaton

Published online by Cambridge University Press:  15 August 2002

Olivier Carton  and
Ramón Maceiras
Olivier Carton
Affiliation:
Institut Gaspard Monge, Université de Marne-la-Vallée, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France; Olivier.Carton@univ-mlv.fr.
Ramón Maceiras
Affiliation:
Institut Gaspard Monge, Université de Marne-la-Vallée, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France; Olivier.Carton@univ-mlv.fr.
Get access

Abstract

The Rabin index of a rational language of infinite words given by a parity automaton with n states is computable in time O(n2c) where c is the cardinality of the alphabet. The number of values used by a parity acceptance condition is always greater than the Rabin index and conversely, the acceptance condition of a parity automaton can always be replaced by an equivalent acceptance condition whose number of used values is exactly the Rabin index. This new acceptance condition can also be computed in time O(n2c).

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 6 , November 1999 , pp. 495 - 505
Copyright
© EDP Sciences, 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

J.R. Büchi, On a decision method in the restricted second-order arithmetic, in Proc. Int. Congress Logic, Methodology and Philosophy of science, Berkeley 1960, Stanford University Press (1962) 1-11.
Carton, O., Chain automata. Theoret. Comput. Sci. 161 (1996) 191-203. CrossRef
E.A. Emerson and C.S. Jutla, Tree automata, Mu-calculus and determinacy, in Proc. 32th Symp. on Foundations of Computer Science (1991) 368-377.
Krishnan, S.C., Puri, A. and Brayton, R.K., Structural complexity of ω-languages, in STACS '95, Springer-Verlag, Lectures Notes in Comput. Sci. 900 (1995) 143-156. CrossRef
McNaughton, R., Testing and generating infinite sequences by a finite automaton. Inform. Control 9 (1966) 521-530. CrossRef
Mostowski Regular, A. expressions for infinite trees and a standard form for automata, in Computation theory, A. Skowron, Ed., Springer-Verlag, Berlin, Lectures Notes in Comput. Sci. 208 (1984) 157-168. CrossRef
Mostowski, A., Hierarchies of weak automata and weak monadic formulas. Theoret. Comput. Sci. 83 (1991) 323-335. CrossRef
D. Muller, Infinite sequences and finite machines, in Switching Theory and Logical Design, P. of Fourth Annual IEEE Symp., Ed. (1963) 3-16.
Rabin, M.O., Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc. 141 (1969) 1-35.
Tarjan, R.E., Depth first search and linear graphs. SIAM J. Comput. 1 (1972) 146-160. CrossRef
W. Thomas, Automata on infinite objects, in Handbook of Theoretical Computer Science, J. van Leeuwen, Ed., B (Elsevier, 1990) Chapter 4, pp. 133-191.
Wagner, K., Eine topologische Charakteriesierung einiger Klassen regulärer Folgenmengen. Elektron. Informationsverarb. Kybernet. 13 (1977) 505-519.
Wagner, K., On ω-regular sets. Inform. Control 43 (1979) 123-177. CrossRef
Wilke, T. and Yoo, H., Computing the Wadge degree, the Lipschitz degree, and the Rabin index of a regular language of infinite words in polynomial time, in Trees in Algebra and Programming - CAAP '95 P. M. et al., Ed., Springer-Verlag, Lectures Notes in Comput. Sci. 915 (1995) 288-302. CrossRef
Wilke, T. and Yoo, H., Computing the Rabin index of a regular language of infinite words. Inform. Comput. 130 (1996) 61-70. CrossRef