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Abstract

As is well known, any function of the two-valued algebra of logic (FAL) can be realized in the basis &, V, ˥ by a scheme of depth 2 (if by depth we understand the maximal number of alternations of the operators & and V). Such a scheme is obtained in modeling normal forms of FAL [1]. With this, an asymptotic bound on the complexity of the scheme equals n·2n−1, where n is the number of variables. Lupanov [2] showed that any FAL is realized in basis &, V, ˥ by a scheme of depth 3 with asymptotic bound on its complexity of 2n/log2n. With a further increase in depth, this bound is not changed.

Keywords

Load Factor Minimal Depth Disjunctive Normal Form Input Element Elementary Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

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    N. E. Kobrinskii and B. A. Trakhtenbrot, Introduction to the Theory of Finite Automata, Fizmatgiz (1962).Google Scholar
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    O. B. Lupanov, “On the realization of functions of the algebra of logic by formulas of finite class (formulas of bounded depth) in the basis &, V,” in: Problems of Cybernetics, Vol. 6, Fizmatgiz (1961).Google Scholar
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Copyright information

© Consultants Bureau, New York 1969

Authors and Affiliations

  • Ya. I. Fet

There are no affiliations available

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