Experimental comparison of the effectiveness of programs for minimizing systems of Boolean functions in the class of disjunctive normal forms

Abstract

Objectives. Methods, algorithms and programs for solving problems of minimizing the DNF representations of Boolean functions are widely used in the design of digital systems to reduce the complexity (crystal area) of functional combinational blocks of digital systems placed into digital VLSI.The objective of the work is experimental comparison of domestic programs for minimizing Boolean functions in the DNF class included in the FLC-2 with two well-known foreign freely distributed programs for minimizing DNF known as Espresso IIC and ABC.Methods. Four sets sample of input data were used to compare the programs – there are widely known examples on which the effectiveness of the Espresso IIC program was tested and two sets of industrial examples from the practice of designing the logic circuits. Algorithms and programs for parallelization of calculations when separate functions of minimizing have been developed. Software tools for the application of joint minimization programs with separate minimization of functions are proposed.Results. The areas of preferred use and the execution time of programs for the source systems of functions (for minimization) characterized by large parameter values of dozens of arguments and functions, tens of thousands of elementary conjunctions are revealed. The efficiency of application of minimization programs for various forms of input data assignment is investigated – DNF, orthogonalized DNF, BDD (Binary Decision Diagrams) representations for systems of functions, truth tables and perfect DNF systems.Conclusion. The experimental results show the effectiveness of parallel programs – reducing the calculation time and increasing the dimensions of solved problems of separate minimization of Boolean function systems.