Threshold Logic

Sze-Tsen Hu

• Publisher: University of California Press
• Year: 2023
• Print ISBN: 9780520329553
• eBook ISBN: 9780520329560
• Edition: 1
• Topic: Mathematics
• Subtopic: Logic in Mathematics
• Index: Mathematics

Threshold Logic by Sze-Tsen Hu offers the first comprehensive treatment of logical elements based on the threshold principle, devices that had attracted growing attention in the wake of McCulloch and Pitts’s 1943 neuron models and von Neumann’s investigations into reliability. Threshold devices—including paramétrons, magnetic core switches, and Esaki diode circuits—function as complex logical units that extend well beyond the simplicity of “AND” and “OR” gates. Because a single device can generate relatively intricate switching functions, they hold the potential to increase the speed and efficiency of electronic digital computers while reducing the number of components required. This efficiency has made threshold logic a key subject in computing research during the postwar era, and the book situates the field at the intersection of mathematical theory, hardware design, and computational application.

Hu’s study surveys and advances work in three major areas: defining the conditions a switching function must meet to qualify as a threshold function, devising algorithms to test and implement these functions, and developing synthesis methods for networks composed of threshold gates. The book is designed both as a reference consolidating contributions from the previous decade and as a research monograph introducing Hu’s own results, much of which had been confined to Lockheed Missiles and Space Company technical reports. The early chapters cover the theory of threshold functions and decision conditions; subsequent chapters detail algorithms for classification and realization; the concluding chapter presents Hu’s mathematically rigorous process for constructing minimal threshold networks, moving beyond the heuristic techniques that had dominated the field. With an eye to accessibility, Hu deliberately emphasizes clarity in his proofs and explanations, ensuring that both engineers and mathematicians can use the book as a foundation for further exploration of threshold logic in the design of high-speed computing systems.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1965.

Table of contents

• Cover
• PREFACE
• CONTENTS
• SPECIAL SYMBOLS AND ABBREVIATIONS
• Chapter I: SWITCHING FUNCTIONS
• Chapter II: THRESHOLD FUNCTIONS
• Chapter III: MONOTONICITY AND ASUMMABILITY
• Chapter IV: CLASSIFICATION
• Chapter V: ARITHMETIC INVARIANTS
• Chapter VI: SYNTHESIS OF LINEAR SEPARABILITY
• Chapter VII: MINIMAL SEPARATING SYSTEMS
• Chapter VIII: MINIMAL THRESHOLD NETWORKS
• Bibliography
• Index