Synthesis of Multi-Level Dual Reed-Muller Expressions

This paper introduces the fundamental theory, algorithms, and terminology regarding synthesis of multi, level Dual Reed-Muller expressions. The increasing interest in using Dual Reed-Muller expressions as a way of representing and manipulating switching functions, and as a mean of designing circuits based on OR/XNOR gates has led to this research. Up to present there are only two-level Dual Reed-Muller minimization algorithms in use, although the need for multi-level minimization algorithms has been recognized. A new theory and algorithms for multi-level Dual Reed-Muller minimization have been developed. It introduces a Dual Reed-Muller factored form and uses algebraic algorithms for factorization decomposition, re-substitution, and extraction of common cubes and sub-expressions.