ESOP Expression Minimization for Multi-Valued Functions Using Nonlinear Integer Programming

The minimization of Exclusive-OR Sum-of-Products (ESOP) expressions in the case of multi-valued input, multi-output binary, and certain types of multi-valued output functions (MVESOP) is approached in this work through a novel nonlinear integer programming methodology. The devised method is applicable to both completely and incompletely specified functions and has the capacity to provide exact solutions of global optimality. A key general transformation converts the minimization problem from the MVESOP to the classical algebraic domain, resulting in a nonlinear integer program. Notably, for the challenging cases of incompletely specified functions, the problem becomes significantly simpler after this mapping. Several illustrative, analytical, and numerical examples are provided to demonstrate the implementation and performance of the approach.