An entropy measure for the complexity of multi-output Boolean functions

Abstract

Entropy measures are examined in view of the current logic synthesis methodology. The complexity of a Boolean function can be expressed in terms of computational work. Experimental data are presented in support of the entropy definition of computational work based upon the input-output description of a Boolean function. These data show a linear relationship between the computational work and the average number of literals in a multilevel implementation. The investigation includes single-output and multioutput function with and without don't care states. The experiments conducted on a large number of randomly generated functions showed that the effect of don't cares is to reduce the computational work. For several finite state machine benchmarks, the computational work gave a good estimate of the size of the circuit. Circuit delay is shown to have a nonlinear relationship to the computational work.<>