Associative digital network theory: an associative algebra approach to logic, arithmetic and state machines

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 innew 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 yieldsplanar 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 INDICE: Part 1 – Sequential Logic: Finite Associative Closure. 1 Introduction. 2 Simple Semigroups and the Five Basic Machines. 3 Coupling State Machines. 4 General Network Decomposition of State Machines. Part 2 – Combinational Logic: Associative, Commuting Idempotents. 5 Symmetric and Planar Boolean LogicSynthesis. 6 Fault Tolerant Logic with Error Correcting Codes. Part 3 – Finite Arithmetic: Associative, commutative. 7 Fermat’s Small Theorem extended to rp-1 mod p3. 8 Additive structure of units group mod pk, with carry extension for a proof of Fermat’s Last Theorem. 9 From the additive structure of Z(.) modmk (squarefree) to a proof of Goldbach’s conjecture. 10 Powersums Sxp represent residues mod pk, from Fermat to Waring. 11 Log-arithmetic, with single and dual base. Bibliography. Index.

• ISBN: 978-1-4020-9828-4
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 200
• Fecha Publicación: 01/04/2009
• Nº Volúmenes: 1
• Idioma: Inglés