Journal ArticleDOI
Generalization of Consensus Theory and Application to the Minimization of Boolean Functions
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The consensus is extended from two to any number of terms, and it is shown that any prime implicant of a Boolean function is a generalized consensus; therefore the algorithm for the determination of the consensus relations can be used for finding theprime implicants.Abstract:
Given two implicants of a Boolean function, we can, by performing their consensus, find a third implicant. This operation has been used for finding the prime implicants of a Boolean function. In this paper, the consensus is extended from two to any number of terms. A property of these generalized consensus relations leads to a systematic way of finding them. It is shown that any prime implicant of a Boolean function is a generalized consensus; therefore the algorithm for the determination of the consensus relations can be used for finding the prime implicants. This new method is simpler than the usual process of iterative consensus. It is also shown in this paper that consensus theory can be used for finding the minimal sums of a Boolean function. The methods are applicable for any Boolean function, with or without don't care conditions, with a single or a multiple output.read more
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References
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Journal ArticleDOI
Minimization of Boolean functions
TL;DR: A systematic procedure is presented for writing a Boolean function as a minimum sum of products and specific attention is given to terms which can be included in the function solely for the designer's convenience.
Journal ArticleDOI
The Problem of Simplifying Truth Functions
TL;DR: The Problem of Simplifying Truth Functions is concerned with the problem of reducing the number of operations on a graph to a simple number.
Journal ArticleDOI
A Way to Simplify Truth Functions
TL;DR: In this paper, a way to simplify truth functions is proposed. But it is difficult to verify the correctness of truth functions and it is not easy to find the truth functions in practice.
Journal ArticleDOI
Irredundant disjunctive and conjunctive forms of a Boolean function
TL;DR: A thorough algebraic method is described for the determination of the complete set of irredundant normal and conjunctive forms of a Boolean function that is mechanical and therefore highly programmable on a computer.
Journal ArticleDOI
Determination of the Irredundant Normal Forms of a Truth Function by Iterated Consensus of the Prime Implicants
TL;DR: By applying repeatedly the rule of consensus to the prime implicants, it is possible to derive alist of implication relations that express the necessary and sufficient conditions of eliminability of the primeimplicants in terms of which the irredundant normal forms can be computed.