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Date: 17-11-2021
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The mathematical study of abstract computing machines (especially Turing machines) and the analysis of algorithms used by such machines.
A connection between automata theory and number theory was provided by Christol et al. (1980), who showed that a sequence is generated by a -automaton iff the formal power series with coefficients is algebraic on the field of rational elements , where and are polynomials with coefficients in the finite field .
REFERENCES:
Christol, G.; Kamae, T.; Mendès-France, M.; and Rauzy, G. "Suites Algébriques, automates et substitutions." Bull. Soc. Math. France 108, 401-419, 1980.
Harrison, M. A. Introduction to Switching and Automata Theory. New York: McGraw-Hill, p. 188, 1965.
Simon, M. Automata Theory. Singapore: World Scientific, 1999.
Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, 2002.
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