Cited By
View all- Gilman R(1984)Computations with rational subsets of confluent groupsEUROSAM 8410.1007/BFb0032843(207-212)Online publication date: 1984
Free groups and regular expressions
Pages 113 - 128
Abstract
Group events are defined as regular events recognized by partial group automata. Canonical forms are introduced for the class of regular expressions denoting group events. Algorithms are presented to find a canonical form from a recognizing automaton, to find a recognizing automaton from a canonical form, and to find a canonical form from a regular expression denoting a simple group event. Furthermore an algorithm is presented that decides whether or not two canonical forms denote the same event.
References
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J. A. Brzozowski: "Roots of Star Events," Journal of the Association of Computing Machinery, Vol. 14, No. 3, July, 1967, pp. 466-477.
[2]
S. Ginsburg: An Introduction to Mathematical Machine Theory. Addison-Wesley, 1962.
[3]
M. Hall: The Theory of Groups, The MacMillan Company, 1961.
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M. A. Harrison: Introduction to Switching and Automata Theory, McGraw Hill, 1965.
[5]
S. C. Kleene: Representation of Events in Nerve Nets and Finite Automata, Automata Series, Princeton University Press, 1956.
[6]
J. Nielsen: "Om regning med ikke-kom-mutative faktorer og dens anvendelse i gruppeteorien," Matematisk Tidsskrift B (1921), pp. 77-94.
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O. Schreir: "Die Untergruppen der freien Gruppen," Abh. aus dem Math. Seminar der Hamburgischen Unlversität 5, pp. 161-183.
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J. Hartmanis and R. E. Stearns: Algebraic Structure Theory of Sequential Machines, Prentice Hall, 1966.
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K. K. Krohn and J. L. Rhodes: "Algebraic Theory of Machines," Proc. of Symposium on Mathematical Theory of Automata, Polytechnic Press, 1963.
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Published In
May 1969
267 pages
ISBN:9781450374781
DOI:10.1145/800169
Copyright © 1969 ACM.
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Published: 05 May 1969
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View all- Gilman R(1984)Computations with rational subsets of confluent groupsEUROSAM 8410.1007/BFb0032843(207-212)Online publication date: 1984
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