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Generating Essential Primes for a Boolean Function with Multiple-Valued Inputs

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1 Author(s)
Kuo, Y.S. ; 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.

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Computers, IEEE Transactions on  (Volume:C-36 ,  Issue: 3 )