Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T07:42:54.800Z Has data issue: false hasContentIssue false
  • English
  • Français

Axiomatizing omega and omega-op powers of words

Published online by Cambridge University Press:  15 March 2004

Stephen L. Bloom  and
Zoltán Ésik
Stephen L. Bloom
Affiliation:
Department of Computer Science Stevens Institute of Technology Hoboken, NJ 07030; [email protected].
Zoltán Ésik
Affiliation:
Institute for Informatics University of Szeged 6720 Szeged, Hungary
Get access

Abstract

In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 38 , Issue 1 , January 2004 , pp. 3 - 17
Copyright
© EDP Sciences, 2004

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

Bedon, N., Finite automata and ordinals. Theoret. Comput. Sci. 156 (1996) 119-144. CrossRef
Bedon, N. and Carton, O., Eilenberg, An theorem for words on countable ordinals, in Latin'98: Theoretical Informatics, edited by C.L. Lucchesi and A.V. Moura. Lect. Notes Comput. Sci. 1380 (1998) 53-64. CrossRef
Bloom, S.L. and Choffrut, C., Long words: the theory of concatenation and ω-power. Theoret. Comput. Sci. 259 (2001) 533-548. CrossRef
S.L. Bloom and Z. Ésikn, Iteration Theories. Springer (1993).
Bloom, S.L. and Ésik, Z., Deciding whether the frontier of a regular tree is scattered. Fundamenta Informaticae 55 (2003) 1-21.
Bruyère, V. and Carton, O., Automata on linear orderings, in Proc. Mathematical Foundations of Computer Science. Lect. Notes Comput. Sci. 2136 (2001) 236-247. CrossRef
V. Bruyère and O. Carton, Hierarchy among automata on linear orderings, in Foundation of Information Technology in the Era of Network and Mobile Computing, Proc. TCS 2002. Kluwer Academic Publishers (2002) 107-118.
J.R. Büchi, On a decision method in restricted second-order arithmetic, in Int. Congress Logic, Methodology, and Philosophy of Science, Berkeley, 1960. Stanford University Press (1962) 1-11.
J.R. Büchi, Transfinite automata recursions and weak second order theory of ordinals, in Int. Congress Logic, Methodology, and Philosophy of Science, Jerusalem, 1964. North Holland (1965) 2-23.
Choueka, Y., Finite automata, definable sets, and regular expressions over ωn -tapes. J. Comp. Syst. Sci. 17 (1978) 81-97. CrossRef
Courcelle, B., Frontiers of infinite trees. RAIRO: Theoret. Informatics Appl./Theor. Comput. Sci. 12 (1978) 319-337.
Ésik, Z. and Labella, A., Equational properties of iteration in algebraically complete categories. Theoret. Comput. Sci. 195 (1998) 61-89. CrossRef
Heilbrunner, S., An algorithm for the solution of fixed-point equations for infinite words. RAIRO: Theoret. Informatics Appl. 14 (1980) 131-141.
J.B. Rosenstein, Linear Orderings. Academic Press, New York (1982).
Thomas, W., On frontiers of regular trees. RAIRO: Theoret. Informatics Appl. 20 (1986) 371-381.
Th. Wilke, An algebraic theory for regular languages of finite and infinite words. Int. J. Algebra Comput. 3 (1993) 447-489. CrossRef
Wojciechowski, J., Finite automata on transfinite sequences and regular expressions. Fundamenta Informaticae 8 (1985) 379-396.