Journal ArticleDOI
A Prime Implicant Algorithm with Factoring
B.L. Hulme,R.B. Worrell +1 more
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It is shown that factoring accounts for a dramatic increase in efficiency over Nelson's algorithm, and the increased efficiency is illustrated with results obtained from several examples that were implemented for both algorithms using the symbolic manipulation systems SETS.Abstract:
An algorithm for finding the prime implicants of a Boolean function is given. The algorithm is similar to Nelson's algorithm since both involve the operations of complementing, expanding, and simplifying, but the new algorithm includes the additional operation of factoring. The algorithm with factoring is proved, and it is shown that factoring accounts for a dramatic increase in efficiency over Nelson's algorithm. The increased efficiency is illustrated with timing results obtained from several examples that were implemented for both algorithms using the symbolic manipulation systems SETS.read more
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References
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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
Generalization of Consensus Theory and Application to the Minimization of Boolean Functions
TL;DR: 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.
Journal ArticleDOI
A New Algorithm for Generating Prime Implicants
TL;DR: It is proved that the algorithm will find all the prime implicants of a Boolean function, and the algorithm is implemented by a computer program in the LISP language.
Journal ArticleDOI
Simplest Normal Truth Functions
TL;DR: This paper develops a method for both disjunctive and conjunctive normal truth functions which is in some respects similar to Quine's but which does not involve prior expansion of a formula into developed normal form.