Abstract
In the synthesis of circuits realizing Boolean functions it is important to construct minimal circuits. Some results in this direction were obtained by Cardot [5], who proved the minimality of relay contact circuits for a sum of n variables modulo-2, whereas Soprunenko [3] obtained a minimal realization of conjunctions and disjunctions with the aid of circuits of functional elements in a base consisting of Sheffer’s stroke.
Original article submitted March 15, 1969.
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Literature Cited
O. B. Lupanov, “Synthesis of certain classes of control systems,” Problemy Kibernetiki, Vol, 10, Fizmatgiz, Moscow (1963), pp. 63–97.
O. B. Lupanov, “A method of synthesis of control systems — the principle of local coding,” Problemy Kibernetiki, Vol. 14, Nauka, Moscow (1965), pp. 31–110.
E. P. Soprunenko, “Minimal realization of functions by circuits using functional elements,” Vol. 15, Problemy Kibernetiki, Nauka, Moscow (1965), pp. 117–134.
S. V. Yablonskii, “Functional constructions in k-valued logic,” Proc. Steklov Mathematical Institute of the Academy of Sciences of the USSR, 51:5–142 (1958).
C. Cardot, “Some results concerning the use of Boolean algebra in the synthesis of relay contact circuits,” Annales des Télécommunications, 7(2):75–84 (1952).
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© 1973 Consultants Bureau, New York
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Red’kin, N.P. (1973). Proof of Minimality of Circuits Consisting of Functional Elements. In: Lyapunov, A.A. (eds) Systems Theory Research. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-0079-4_4
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DOI: https://doi.org/10.1007/978-1-4757-0079-4_4
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