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Generating Essential Primes for a Boolean Function with Multiple-Valued Inputs
March 1987 (vol. 36 no. 3)
pp. 356-359
Y.S. Kuo, Institute of Information Science
Detecting essential primes is important in multiple-valued logic minimization. In this correspondence, we present a fast algorithm that can generate all essential primes without generating a prime cover of the Boolean function. A new consensus operation called asymmetric consensus (acons) is defined. In terms of acons, we prove a necessary and sufficient condition for detecting essential primes for a Boolean function with multiple-valued inputs. The detection of essential primes can be performed by using a tautology checking algorithm. We exploit the unateness of a Boolean function to speed up tautology checking. The notion of unateness considered is more general than that has appeared in the literature.
Index Terms:
unate function, Boolean function with multiple-valued inputs, consensus, essential prime implicant, logic minimization, tautology checking
Y.S. Kuo, "Generating Essential Primes for a Boolean Function with Multiple-Valued Inputs," IEEE Transactions on Computers, vol. 36, no. 3, pp. 356-359, March 1987, doi:10.1109/TC.1987.1676907
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