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A Census of Finite Automata

Published online by Cambridge University Press:  20 November 2018

Michael A. Harrison
Michael A. Harrison*
Affiliation:
University of California, Berkeley
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A finite automaton may be thought of as a possible abstraction of a digital computer. Imagine a tape or sequence of letters from some alphabet being fed into a device with a finite number of internal states. When the device is in a particular state and receives an input letter, the system passes to another internal state and prints a letter on an output tape. This operation is continued until the entire input sequence has been processed.

Both Harary (6) and Ginsburg (4) have focused attention on the previously unsolved problem of counting the number of equivalence classes of finite automata. In the present paper, this problem is solved completely by proving a variety of theorems about the enumeration of functions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 100 - 113
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Burnside, W., Theory of groups of finite order (Cambridge, 1911).Google Scholar
2. Davis, R. L., The number of structures of finite relations, Proc. Amer. Math. Soc., 4 (1953), 486–495.Google Scholar
3. de Bruijn, N. G., Generalization of Pölya's fundamental theorem in enumerative combinational analysis, Nederl. Akad. Wetensch. Proc. Ser. A., 52 (1959), 59–69.Google Scholar
4. Ginsburg, S., An introduction to mathematical machine theory (Reading, Mass., 1962).Google Scholar
5. Harary, F., On the number of bi-colored graphs, Pacific J. Math., 8 (1958), 743–755.Google Scholar
6. Harary, F., Unsolved problems in the enumeration of graphs, Magyar Tud. Akad. Mat. Kutatö Int. Közl, 5 (1960), 63–95.Google Scholar
7. Harary, F., The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc, 78 (1955), 445–463.Google Scholar
8. Harrison, M. A., Combinatorial problems in Boolean algebras and applications to the theory of switching, Ph.D. Thesis (Ann Arbor, 1963).Google Scholar
9. Pölya, G., Kombinatorische Anzahlbestimmungen für Gruppen, Graphen, und chemische Verbindungen, Acta Math., 68 (1937), 145–254.Google Scholar