Recent Developments in Switching Theory

Recent Developments in Switching Theory

1st Edition - January 1, 1971

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  • Editor: Amar Mukhopadhyay
  • eBook ISBN: 9781483218816

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Electrical Science Series: Recent Developments in Switching Theory covers the progress in the study of the switching theory. The book discusses the simplified proof of Post's theorem on completeness of logic primitives; the role of feedback in combinational switching circuits; and the systematic procedure for the design of Lupanov decoding networks. The text also describes the classical results on counting theorems and their application to the classification of switching functions under different notions of equivalence, including linear and affine equivalences. The development of abstract harmonic analysis of combinational switching functions; the theory of universal logic modules, methods of their construction, and upper bounds on the input terminals; and cellular logic are also considered. The book further tackles the systematic techniques for the realization of multi-output logic function by means of multirail cellular cascades; the programmable cellular logic; and the logical design of programmable arrays. Electrical engineers, electronics engineers, computer professionals, and student taking related courses will find the book invaluable.

Table of Contents

  • Contents

    List of Contributors



    I. Complete Sets of Logic Primitives

    I. Introduction

    II. Iteratively Closed System of Functions

    III. Characterization of Weak Complete Set of Logic Primitives

    IV. Reduction Theorems

    V. Theorem of Post

    VI. Bases and Simple Bases

    VII. Almost Complete Sets of Logic Primitives

    Appendix. Proof of Theorem 7.1


    II. Combinational Circuits with Feedback

    I. Introduction

    II. Circuit Visualization of Markov's Result

    III. A Circuit with a Single Not-Element Which Inverts Two Variables

    IV. The Design of "Multi-Inversion" Circuits Which Use Only One Inverter

    V. Proof of the Necessity of Unstable Circuit Equilibria

    VI. A "Multi-Inversion" Circuit Which Is Stable

    VII. Summary and Conclusions


    III. Lupanov Decoding Networks

    I. Introduction

    II. Disjunctive and Nondisjunctive Complete Decoding Networks

    III. The Case When r≠2ᴷ

    IV. The Optional Terms

    V. Toward a General Theory

    VI. Conclusions


    IV. Counting Theorems and their Applications to Classification of Switching Functions

    I. Introduction to Boolean Functions and Classification Problems

    II. Group Theory and Polya's Theorem

    III. Some Applications of Polya's Theorem to Switching Functions

    IV. Structure Theorems for Permutation Groups and the Determination of Cycle Indices

    V. Operations on the Range, Genera, and a Lower Bound

    Appendix 1. Cycle Index Polynomials for Sn

    Appendix 2. Cycle Index Polynomials for Gn

    Appendix 3. Cycle Index Polynomials for GLn(W2)

    Appendix 4. Cycle Index Polynomials for An(Z2)


    V. Harmonic Analysis of Switching Functions

    I. Summary

    II. Survey of Abstract Harmonic Analysis

    III. Combinatorial Applications

    IV. Analysis of the Prototype Equivalence Relation

    V. Synthesis of Encoded Input Logic


    VI. Universal Logic Modules

    I. Statement of the Problem

    II. Bounds for M(n)

    III. The Construction of ULM'S for Small n

    IV. Other Approaches to the Universal Module Problem

    V. Historical References


    VII. Cellular Logic

    I. Introduction

    II. Single-Rail Cascades

    III. Two-Rail Cascades

    IV. Two-Dimensional Arrays

    V. Minimization of Cellular Arrays

    VI. Review of Other Works in Cellular Area


    VIII. The Theory of Multirail Cascades

    I. Introduction

    II. Decomposition Theory of Group Functions

    III. Synthesis of Multirail Cascades


    IX. Programmable Cellular Logic

    I. Introduction

    II. Programmable Cellular Arrays

    III. Arrays for Arbitrary Logic

    IV. Special-Purpose Arrays

    V. Conclusion


    Author Index

    Subject Index

Product details

  • No. of pages: 454
  • Language: English
  • Copyright: © Academic Press 1971
  • Published: January 1, 1971
  • Imprint: Academic Press
  • eBook ISBN: 9781483218816

About the Editor

Amar Mukhopadhyay

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