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.
Contents List of Contributors Preface Acknowledgments 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 References 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 References 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 References 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) References V. Harmonic Analysis of Switching Functions I. Summary II. Survey of Abstract Harmonic Analysis III. Combinatorial Applications IV. Analysis of the Prototype Equivalence Relation
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- © Academic Press 1971
- 1st January 1971
- Academic Press
- eBook ISBN: