Mathematical Theory of Switching Circuits and Automata


Book Description

By applying Boolean algebra to the designing of circuits, C. E. Shannon practically created the switching theory which is necessary to the development of electronic computers. For the next three decades much research was done and most of the major problems of logical design were solved. Recent interest having focused on the purely theoretical aspects of computer and logical networks, Hu now believes that the time has come for a consolidation of the mathematical foundations of the subject. In the present book the author accordingly undertakes to establish a new branch of pure mathematics with a uniform notation and terminology by organizing the past research results into a form usable to both mathematicians and engineers, while simplifying theory by stripping it of complex "hardware" considerations as well as of all unnecessary advanced mathematics. A number of exercises have been provided at the end of each chapter. 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 1968.













Encyclopedia of Computer Science and Technology


Book Description

"This comprehensive reference work provides immediate, fingertip access to state-of-the-art technology in nearly 700 self-contained articles written by over 900 international authorities. Each article in the Encyclopedia features current developments and trends in computers, software, vendors, and applications...extensive bibliographies of leading figures in the field, such as Samuel Alexander, John von Neumann, and Norbert Wiener...and in-depth analysis of future directions."




The Second Age of Computer Science


Book Description

By the end of the 1960s, a new discipline named computer science had come into being. A new scientific paradigm--the 'computational paradigm'--was in place, suggesting that computer science had reached a certain level of maturity. Yet as a science it was still precociously young. New forces, some technological, some socio-economic, some cognitive impinged upon it, the outcome of which was that new kinds of computational problems arose over the next two decades. Indeed, by the beginning of the 1990's the structure of the computational paradigm looked markedly different in many important respects from how it was at the end of the 1960s. Author Subrata Dasgupta named the two decades from 1970 to 1990 as the second age of computer science to distinguish it from the preceding genesis of the science and the age of the Internet/World Wide Web that followed. This book describes the evolution of computer science in this second age in the form of seven overlapping, intermingling, parallel histories that unfold concurrently in the course of the two decades. Certain themes characteristic of this second age thread through this narrative: the desire for a genuine science of computing; the realization that computing is as much a human experience as it is a technological one; the search for a unified theory of intelligence spanning machines and mind; the desire to liberate the computational mind from the shackles of sequentiality; and, most ambitiously, a quest to subvert the very core of the computational paradigm itself. We see how the computer scientists of the second age address these desires and challenges, in what manner they succeed or fail and how, along the way, the shape of computational paradigm was altered. And to complete this history, the author asks and seeks to answer the question of how computer science shows evidence of progress over the course of its second age.




Automata Theory and its Applications


Book Description

The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.




From Boolean Logic to Switching Circuits and Automata


Book Description

Logic networks and automata are facets of digital systems. The change of the design of logic networks from skills and art into a scientific discipline was possible by the development of the underlying mathematical theory called the Switching Theory. The fundamentals of this theory come from the attempts towards an algebraic description of laws of thoughts presented in the works by George J. Boole and the works on logic by Augustus De Morgan. As often the case in engineering, when the importance of a problem and the need for solving it reach certain limits, the solutions are searched by many scholars in different parts of the word, simultaneously or at about the same time, however, quite independently and often unaware of the work by other scholars. The formulation and rise of Switching Theory is such an example. This book presents a brief account of the developments of Switching Theory and highlights some less known facts in the history of it. The readers will find the book a fresh look into the development of the field revealing how difficult it has been to arrive at many of the concepts that we now consider obvious . Researchers in the history or philosophy of computing will find this book a valuable source of information that complements the standard presentations of the topic.




NBS Special Publication


Book Description