On the numbers of variables to represent sparse logic functions

  • Authors:
  • Tsutomu Sasao

  • Affiliations:
  • Kyushu Institute of Technology, Iizuka, Japan

  • Venue:
  • Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
  • Year:
  • 2008

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Abstract

In an incompletely specified function f, don't care values can be chosen to minimize the number of variables to represent f. It is shown that, in incompletely specified functions with k 0's and k 1's, the probability that f can be represented with only p = 2[log2(k + 1)] variables is greater than e-1 = 0.36788. In the case of multiple-output functions, where only the outputs for k input combinations are specified, most functions can be represented with at most p = 2[log2(k+1)] -1 variables. Experimental data is shown to support this. Because of this property, an IP address table can be realized with a small amount of memory.