Exact Minimization of and-EXOR Expressions of Practical Benchmark Functions

We propose faster-computing methods for the minimization algorithm of AND-EXOR expressions, or Exclusive-or Sum-Of-Products expressions (ESOPs), and obtain the exact minimum ESOPs of benchmark functions. These methods improve the search procedure for ESOPs, which is the most time-consuming part of the original algorithm. For faster computation, the search space for ESOPs is reduced by checking the upper and lower bounds on the size of ESOPs. Experimental results to demonstrate the effectiveness of these methods are presented. The exact minimum ESOPs of many practical benchmark functions have been revealed by this improved algorithm.