Generating essential primes for a Boolean function with multiple-valued inputs

  • Authors:

  • Y. S. Kuo;W. K. Chou

  • Affiliations:

  • Institute of Information Science, Academia Sinica, Taipei, Taiwan, The Republic of China;Institute of Information Science, Academia Sinica, Taipei, Taiwan, The Republic of China

  • Venue:
  • DAC '86 Proceedings of the 23rd ACM/IEEE Design Automation Conference
  • Year:
  • 1986

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Abstract

Detecting essential primes is important in multiple-valued logic minimization. In this paper, 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.