Associative Digital Network Theory
An Associative Algebra Approach to Logic, Arithmetic and State Machines
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Beschreibung
Associative Digital Network Theory is intended for researchers at industrial laboratories,
teachers and students at technical universities, in electrical engineering, computer science and applied mathematics departments, interested in new developments of modeling and designing digital networks (DN: state machines, sequential and combinational logic) in general, as a combined math/engineering discipline. As background an undergraduate level of modern applied algebra (Birkhoff-Bartee: Modern Applied Algebra - 1970, and Hartmanis-Stearns: Algebraic Structure of Sequential Machines - 1970) will suffice. Essential concepts and their engineering interpretation are introduced in a practical fashion with examples. The motivation in essence is: the importance of the unifying associative algebra of function composition (viz. semigoup theory) for the practical characterisation of the three main functions in computers, namely sequential logic (state-machines), arithmetic and combinational (Boolean) logic.
This book presents a unifying math/engineering approach to the main computer functions of combinatorial logic, arithmetic and state-machines. Essential concepts and their engineering interpretation are introduced in a practical fashion that includes examples.
Associative Digital Network Theory is intended for researchers at industrial laboratories,
teachers and students at technical universities, in electrical engineering, computer science and applied mathematics departments, interested in new developments of modeling and designing digital networks (DN: state machines, sequential and combinational logic) in general, as a combined math/engineering discipline. As background an undergraduate level of modern applied algebra (Birkhoff-Bartee: Modern Applied Algebra - 1970, and Hartmanis-Stearns: Algebraic Structure of Sequential Machines - 1970) will suffice.
Essential concepts and their engineering interpretation are introduced in a practical fashion with examples. The motivation in essence is: the importance of the unifying associative algebra of function composition (viz. semigoup theory) for the practical characterisation of the three main functions in computers, namely sequential logic (state-machines), arithmetic and combinational (Boolean) logic.
A unifying math/engineering approach to the basic computer functions: - combinational logic, arithmetic and state machines
Boolean logic spectral analysis yields planar mapping in Silicon VLSI technology
A residue-and-carry method allows proving the conjectures of Fermat and Goldbach
New binary coded log-arithmetic, and VLSI implementation, are described
The five basic state machines (BSM) are derived via their sequential closure
State-machine synthesis as coupled BSM network by a new semigroup method
Autor*in
Nico F. Benschop
Themen in »Associative Digital Network Theory«
Algebraic structure Alphabet Digital Lattice Partition Sequential Logic VLSI algebra associative algebra computer computer science electrical engineering logic mathematics microprocessor
Stimmen zu »Associative Digital Network Theory«
From the reviews:"Benschop develops this thesis in an idiosyncratic fashion, reinforced by a long career of practical experience. This book may well be an important historical document, also useful for seminars … . There are profuse illustrations in classic number theory, as well as claims that the outlook sheds new light on classic problems such as those of Fermat and Goldbach, interpreted as machines. … it makes for an interesting book." (Harvey Cohn, ACM Computing Reviews, August, 2009)“The book presents new ways for modeling digital networks (state machines, sequential and combinational logic). It contains applications for known principles of the discrete mathematics. … book also presents new ideas on the finite additive number theory and a binary logarithmetic microprocessor. This book can be very useful for students and professors and also for researchers interested in the digital network theory. It covers a lot of fields, ranging from electrical engineering to computer science and applied mathematics.” (Eleonor Ciurea, Zentralblatt MATH, Vol. 1169, 2009)
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