Logical Minimization of Multilevel Representations of Boolean Function Systems

A decisive influence on complexity and speed of a combinational logic circuit of library CMOS elements is exerted by the preliminary stage of technologically independent optimization of the implemented system of Boolean functions. At present, the main methods of such optimization in the logical synthesis of custom CMOS VLSI blocks are methods for minimizing binary decision diagrams — Binary Decision Diagrams (BDD) or their modifications. Graphical representations of BDD are built on the basis of the Shannon expansions of Boolean functions. A BDD graph corresponds to a set of interrelated Shannon expansion formulas that form a multilevel representation of the minimized system of Boolean functions. The efficiency of applying various optimization procedures of minimization for several types of BDD representations of systems of Boolean functions is investigated in the paper. 7hese procedures are used as a technologically independent optimization in the synthesis of multi-output logic circuits of library CMOS elements. In addition to single logical optimization procedures, sequences of such procedures are studied that form various methods of logical optimization of multilevel representations of systems of Boolean functions. The results of experiments on 49 examples of systems of Boolean functions are presented. 25 optimization routes have been studied, efficient routes have been determined for various types of specifications of function systems. The obtained experimental results are compared with the known ones. It has been established that to estimate the complexity of optimized algebraic representations of systems of functions, it is advisable to use such a criterion as the total number of literals (variables or their inversions) of Boolean variables.