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

Abstract

Abstract-Theoretical results due to V. Malyugin on linearization of arithmetical models of logical functions are interpreted and refined from the viewpoint of modern techniques of logical design of integral circuits and nearest neighbor technologies.

Secure Pseudo-Random Linear Binary Sequences Generators Based on Arithmetic Polynoms

“…Important advantages for these purposes have redundant arithmetic codes, in particular, so-called AN -codes and residue number systems (RNS) codes. The application of these codes to monitor logical data types and fault tolerance implementing devices became possible with the introduction of logical operations arithmetic expressions [11], in particular linear numerical polynomials (LNP) and modular forms [12].…”

“…Using use of LNP proposed by prof. V.D. Malyugin [11] for the construction of parallel generators PRS possible to reduce the maximum length of realizing polynomial to a value of n + 1, where n -number of arguments of a Boolean function implemented [18]. In this paper, this method is used as the basis for the construction of safe (self-checking, fault-tolerant) generators on the basis of the excess bandwidth RNS.…”

“…At the end of the last century there was formed a new direction parallel logic computation by the arithmetic (numeric) polynomials [11]. In particular received position "Modular arithmetic parallel logic computation" of the unification of the theoretical foundations of RNS [13,14,15] and theoretical foundations of parallel logic computation by the arithmetic of polynomials.…”