Boolean Functions and Computation Models

Peter Clote

ISBN 10: 3540594361 / ISBN 13: 9783540594369

Editore: Springer, Berlin, Springer, 2002

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Neuware - The foundations of computational complexity theory go back to Alan Thring in the 1930s who was concerned with the existence of automatic procedures deciding the validity of mathematical statements. The first example of such a problem was the undecidability of the Halting Problem which is essentially the question of debugging a computer program: Will a given program eventu ally halt Computational complexity today addresses the quantitative aspects of the solutions obtained: Is the problem to be solved tractable But how does one measure the intractability of computation Several ideas were proposed: A. Cobham [Cob65] raised the question of what is the right model in order to measure a 'computation step' , M. Rabin [Rab60] proposed the introduction of axioms that a complexity measure should satisfy, and C. Shannon [Sha49] suggested the boolean circuit that computes a boolean function. However, an important question remains: What is the nature of computa tion In 1957, John von Neumann [vN58] wrote in his notes for the Silliman Lectures concerning the nature of computation and the human brain that . . . logics and statistics should be primarily, although not exclusively, viewed as the basic tools of 'information theory'. Also, that body of experience which has grown up around the planning, evaluating, and coding of complicated logical and mathematical automata will be the focus of much of this information theory. The most typical, but not the only, such automata are, of course, the large electronic computing machines.

Codice articolo 9783540594369

Dati bibliografici

• Titolo: Boolean Functions and Computation Models
• Editore: Springer, Berlin, Springer
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 3540594361
• ISBN 13: 9783540594369
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 236 L x 189 A x 40 P (millimetri) 236 millimetri di larghezza per 189 millimetri di altezza per 40 millimetri di profondità
• Peso: 1064 grammi

Descrizione articolo

Riassunto

The two internationally renowned authors elucidate the structure of "fast" parallel computation. Its complexity is emphasised through a variety of techniques ranging from finite combinatorics, probability theory and finite group theory to finite model theory and proof theory. Non-uniform computation models are studied in the form of Boolean circuits; uniform ones in a variety of forms. Steps in the investigation of non-deterministic polynomial time are surveyed as is the complexity of various proof systems. Providing a survey of research in the field, the book will benefit advanced undergraduates and graduate students as well as researchers.

Dalla quarta di copertina

This textbook presents a survey of research on boolean functions, circuits, parallel computation models, function algebras, and proof systems. Its main aim is to elucidate the structure of "fast" parallel computation. The complexity of parallel computation is emphasized through a variety of techniques ranging from finite combinatorics, probability theory, and finite group theory to finite model theory and proof theory. Nonuniform computation models are studied in the form of boolean circuits, uniform ones in a variety of forms. Steps in the investigation of non-deterministic polynomial time are surveyed as is the complexity of various proof systems.
The book will benefit advanced undergraduate and graduate students as well as researchers in the field of complexity theory.