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Finite automata and their decision problems

Published: 01 April 1959 Publication History

Abstract

Finite automata are considered in this paper as instruments for classifying finite tapes. Each one-tape automaton defines a set of tapes, a two-tape automaton defines a set of pairs of tapes, et cetera. The structure of the defined sets is studied. Various generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined. Some decision problems concerning automata are shown to be solvable by effective algorithms; others turn out to be unsolvable by algorithms.

References

[1]
A. W. Burks and Hao Wang, "The logic of automata," Journal of the Association for Computing Machinery, 4, 193-218 and 279-297 (1957).
[2]
S. C. Kleene, "Representation of events in nerve nets and finite automata," Automata Studies, Princeton, pp. 3-41, (1956).
[3]
W. S. McCulloch and E. Pitts, "A logical calculus of the ideas imminent in nervous activity," Bulletin of Mathematical Biophysics, 5, 115-133 (1943).
[4]
E. F. Moore, "Gedanken-experiments on sequential machines," Automata Studies, Princeton, pp. 129-153 (1956).
[5]
A. Nerode, "Linear automaton transformations," Proceedings of the American Mathematical Society, 9, 541- 544 (1958).
[6]
E. Post, "A variant of a recursively unsolvable problem," Bulletin of the American Mathematical Society, 52, 264- 268 (1946).
[7]
J. C. Shepherdson, "The reduction of two-way automata to one-way automata," IBM Journal, 3, 198-200 (1959).

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    Published In

    cover image IBM Journal of Research and Development
    IBM Journal of Research and Development  Volume 3, Issue 2
    April 1959
    98 pages

    Publisher

    IBM Corp.

    United States

    Publication History

    Published: 01 April 1959
    Received: 08 August 1958

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