Exact Minimization of FPRMs for Incompletely Specified Functions by Using MTBDDs

摘要

Fixed polarity Reed-Muller expressions (FPRMs) exhibit several useful properties that make them suitable for many practical applications. This paper presents an exact minimization algorithm for FPRMs for incompletely specified functions. For an n-variable function with α unspecified minterms there are 2~(n+α) distinct FPRMs, and a minimum FPRM is one with the fewest product terms. To find a minimum FPRM the algorithm requires to determine an assignment of the incompletely specified minterms. This is accomplished by using the concept of integer-valued functions in conjunction with an extended truth vector and a weight vector. The vectors help formulate the problem as an assignment of the variables of integer-valued functions, which are then efficiently manipulated by using multi-terminal binary decision diagrams for finding an assignment of the unspecified minterms. The effectiveness of the algorithm is demonstrated through experimental results for code converters, adders, and randomly generated functions.