Axiomatizing omega and omega-op powers of words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 1, pp. 3-17.

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.

DOI : 10.1051/ita:2004005
Classification : 06F99, 03B25 
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Bloom, Stephen L.; Ésik, Zoltán. Axiomatizing omega and omega-op powers of words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 1, pp. 3-17. doi : 10.1051/ita:2004005. http://archive.numdam.org/articles/10.1051/ita:2004005/

[1] N. Bedon, Finite automata and ordinals. Theoret. Comput. Sci. 156 (1996) 119-144. | MR | Zbl

[2] N. Bedon and O. Carton, An Eilenberg 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. | Zbl

[3] S.L. Bloom and C. Choffrut, Long words: the theory of concatenation and ω-power. Theoret. Comput. Sci. 259 (2001) 533-548. | MR | Zbl

[4] S.L. Bloom and Z. Ésikn, Iteration Theories. Springer (1993). | MR | Zbl

[5] S.L. Bloom and Z. Ésik, Deciding whether the frontier of a regular tree is scattered. Fundamenta Informaticae 55 (2003) 1-21. | MR | Zbl

[6] V. Bruyère and O. Carton, Automata on linear orderings, in Proc. Mathematical Foundations of Computer Science. Lect. Notes Comput. Sci. 2136 (2001) 236-247. | MR | Zbl

[7] 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. | MR | Zbl

[8] 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. | MR

[9] 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. | MR | Zbl

[10] Y. Choueka, Finite automata, definable sets, and regular expressions over ω n -tapes. J. Comp. Syst. Sci. 17 (1978) 81-97. | MR | Zbl

[11] B. Courcelle, Frontiers of infinite trees. RAIRO: Theoret. Informatics Appl./Theor. Comput. Sci. 12 (1978) 319-337. | Numdam | MR | Zbl

[12] Z. Ésik and A. Labella, Equational properties of iteration in algebraically complete categories. Theoret. Comput. Sci. 195 (1998) 61-89. | MR | Zbl

[13] S. Heilbrunner, An algorithm for the solution of fixed-point equations for infinite words. RAIRO: Theoret. Informatics Appl. 14 (1980) 131-141. | Numdam | MR | Zbl

[14] J.B. Rosenstein, Linear Orderings. Academic Press, New York (1982). | MR | Zbl

[15] W. Thomas, On frontiers of regular trees. RAIRO: Theoret. Informatics Appl. 20 (1986) 371-381. | Numdam | MR | Zbl

[16] Th. Wilke, An algebraic theory for regular languages of finite and infinite words. Int. J. Algebra Comput. 3 (1993) 447-489. | MR | Zbl

[17] J. Wojciechowski, Finite automata on transfinite sequences and regular expressions. Fundamenta Informaticae 8 (1985) 379-396. | MR | Zbl

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