Information and logical transformations in Schaeffer and Pierce Bases in Maple

Abstract

One of the tasks of synthesis and analysis of the functioning of combinational devices is the representation of a Boolean function in various bases. The absolute completeness of the use and implementation of various transformations of Boolean functions is impossible without the implementation of transformations into universal bases of Schaeffer (AND-NOT) or Webb (OR-NOT). The Logic library of the Maple computer algebra system allows you to use only the operations &nand (Schaeffer basis) and &nor (Webb basis) to build a model of a digital device. Therefore, there is a need to expand the functionality of the Logic library of the Maple computer algebra system by representing Boolean functions in Schaeffer and/or Pierce (Webb) bases. In this regard, the authors of the article have developed procedures that allow the representation of disjunctive or conjunctive normal forms in the Schaeffer basis or in the Webb basis. The development was carried out taking into account the existing data processing functions and procedures. The article describes the technology of extending the Logic library of the Maple computer algebra system by developed procedures that implement the transformation of a given or received Boolean function in Schaeffer or Webb bases.