An Entropy Measure for the Complexity

The complexity of a Boolean function can be expressed in terms of computational work. We present experimental data in support of the entropy definition of computational work based upon the Inputoutput description of a Boolean function. Our data show a linear relationship between the computational work and the average number of literals in a multi-level implementation. The Investigation includes single-output and multi-output 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. Finally, circuit delay is shown to have a non-linear relationship to the computational work.