A discussion on the history of research in arithmetic and Reed-Muller expressions

Abstract

Abstract-This paper discusses early work by Komamiya in Reed-Muller and arithmetic expressions for switching functions.

Malyugin's Theorems: A New Concept in Logical Control, VLSI Design, and Data Structures for New Technologies

“…Probably, a similar linearization problem was first solved in [16], though general interest in this topic had emerged as early as 1952. (see [17]). A solution in the spectral domain is given in [18,19].…”

“…In certain well-known publications, the linear structure of data is determined using different properties of Boolean functions (logical circuits), which must be preliminarily identified. In 1952, Komamiya [17] used a LAR of the type…”

Representations of Elementary Functions Using Binary Moment Diagrams

“…We conjecture that other decision diagrams based on the arithmetic transform (e.g., ACDD, *BMD, K*BMD) also represent elementary functions efficiently. In the past, many people consider the arithmetic transforms [5,6,8,9,10,12,14,17,18,19]. However, to the best of the authors' knowledge, this paper first considered representations of elementary functions by arithmetic transform.…”

Fast algorithm for computing spectral transforms of Boolean and multiple-valued functions on circuit representation

“…Spectral techniques have multiple applications in logic synthesis, testing and verification [1,2,3,4]. The general approach of spectral techniques is the following: The Boolean domain description of the an n-variable logic function is transformed into a spectral domain description.…”

“…To avoid this difficulty, previous works required a non-redundant, orthogonal representation for the function to be transformed. Truth tables were used in [14], disjoint sum-of-products in [15], ROBDDs in [16], and various derivatives of decision diagrams in [17,Chapter 3.5], [4], [18]. The disadvantage of these methods is that they use a representation based on an explicit or implicit disjoint function cover with its typical excessive memory requirements.…”