Abstract
It is proved that for each nondeterministic ordinal automaton there exists a deterministic ordinal automaton which is equivalent to the original one for all countable ordinals. An upper bound for the number of states of the deterministic automaton is double exponential in the number of states of the nondeterministic automaton.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Rabin, M.O. and Scott, D., Finite Automata and Their Decision Problems, IBM J. Res. Develop., 1959, vol. 3, no. 2, pp. 114–125.
Büchi, J.R., Weak Second-Order Arithmetic and Finite Automata, Z. Math. Logik Grundlagen Math., 1960, vol. 6, pp. 66–92.
Büchi, J.R., On a Decision Method in Restricted Second-Order Arithmetics, Proc. 1960 Int. Congress on Logic, Methodology and Philosophy of Science, Nagel, E., Suppes, P., and Tarski, A., Eds., Stanford, CA: Stanford Univ. Press, 1962, pp. 1–11.
Safra, S., On the Complexity of ω-Automata, in Proc. 29th Ann. Sympos. on Foundations of Computer Science, White Plains, NY, 1988, pp. 319–327.
Muller, D.E., Infinite Sequences and Finite Machines, in Proc. 4th Ann. Sympos. on Switching Circuit Theory and Logical Design, Chicago, IL, 1963, New York: IEEE Press, 1963, pp. 3–16.
McNaughton, R., Testing and Generating Infinite Sequences by a Finite Automaton, Inform. Control, 1966, vol. 9, no. 5, pp. 521–530.
Rabin, M.O., Automata on Infinite Objects and Church’s Problem, Providence, R.I.: Amer. Math. Soc., 1972.
Büchi, J.R., The Monadic Second-Order Theory of ω 1, Decidable Theories II, Müller, G.H. and Siefkes, D., Eds., Lect. Notes Math., vol. 328, Berlin: Springer, 1973, pp. 1–127.
Schützenberger, M.P., A propos des relations rationnelles fonctionnelles, Proc. Int. Colloq. on Automata, Languages and Programming, Paris, France, 1972, Nivat, M., Ed., Amsterdam: North-Holland, 1973, pp. 103–114.
Trakhtenbrot, B.A. and Barzdin’, Ya.M., Konechnye avtomaty (povedenie i sintez), Moscow: Nauka, 1970. Translated under the title Finite Automata; Behavior and Synthesis, Amsterdam: North-Holland, 1973.
Eilenberg, S., Automata, Languages, and Machines, vol. A, New York: Academic, 1974.
Choueka, Y., Theories of Automata on ω-Tapes: A Simplified Approach, J. Comput. System Sci., 1974, vol. 8, pp. 117–141.
Thomas, W., A Combinatorial Approach to the Theory of ω-Automata, Inform. Control, 1981, vol. 48, no. 3, pp. 261–283.
Büchi, J.R., Decision Methods in the Theory of Ordinals, Bull. Amer. Math. Soc., 1965, vol. 71, no. 5, pp. 767–770.
Bedon, N. and Carton, O., An Eilenberg Theorem for Words on Countable Ordinals, Proc. 3rd Latin American Sympos. on Theoretical Informatics (LATIN’98). Campinas, Brazil. April 20–24, 1998, Lucchesi, C.L. and Moura, A.V., Eds., Lect. Notes Comp. Sci, vol. 1380, Berlin: Springer, 1998, pp. 53–64.
Additional information
Original Russian Text © An.A. Muchnik, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49, No. 2, pp. 58–72.
Supported in part by the Russian Foundation for Basic Research, project nos. 09-01-00709 and 12-01-00864.
Rights and permissions
About this article
Cite this article
Muchnik, A.A. Determinization of ordinal automata. Probl Inf Transm 49, 149–162 (2013). https://doi.org/10.1134/S003294601302004X
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S003294601302004X