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.
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Editorial Reviews
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From the reviews: "The monograph gives the most recent and complete description of lower bounds for depth-restricted circuits, and propositional proof systems. … the authors present a research monograph on important subjects and provide many very recent results. I would recommend it for any university library and also for researchers." (Ingo Wegener, The Computer Journal, Vol. 46 (3), 2003)
From the Back Cover
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.
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Inside This Book
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First Sentence:
Many fundamental questions in complexity theory can be formulated as a language recognition problem, where by language L we understand a set of strings over a finite alphabet, say = {0, 1}. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
feasible interpolation property, monotonic boolean circuits, critical truth assignment, many large clauses, matching decision tree, unsatisfiability threshold, switching lemma, random restriction method, total truth assignments, oracle registers, calculus refutations, weak recursion, higher type functionals, first moment method, bounded quantifier formulas, propositional proof systems, bounded recursion, polynomial calculus, partial truth assignment, unset variables, bounded minimization, bad graphs, ramified recurrence, random formula, conquer recursion Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercises Exercise, Connection Machine, Parallel Machine Model, Mix Barrington, Prove Lenuna, Use Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Many fundamental questions in complexity theory can be formulated as a language recognition problem, where by language L we understand a set of strings over a finite alphabet, say = {0, 1}. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
feasible interpolation property, monotonic boolean circuits, critical truth assignment, many large clauses, matching decision tree, unsatisfiability threshold, switching lemma, random restriction method, total truth assignments, oracle registers, calculus refutations, weak recursion, higher type functionals, first moment method, bounded quantifier formulas, propositional proof systems, bounded recursion, polynomial calculus, partial truth assignment, unset variables, bounded minimization, bad graphs, ramified recurrence, random formula, conquer recursion Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercises Exercise, Connection Machine, Parallel Machine Model, Mix Barrington, Prove Lenuna, Use Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 44
books:
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21
books
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- Computer Science: A Breadth-First Approach with C by John Impagliazzo on 4 pages
- Computer Science by Richard Jones in Front Matter, and Back Matter
- The Probabilistic Method (Wiley Series in Discrete Mathematics and Optimization) by Noga Alon in Back Matter (1), and Back Matter (2)
- Structure in Complexity Theory (Lecture Notes in Computer Science) by Alan L. Selman in Back Matter (1), and Back Matter (2)
- Proof Theory (Studies in Logic and the Foundations of Mathematics) by Gaisi Takeuti on page 406, and Back Matter
See all 44 books this book cites
- The Parametric Lambda Calculus: A Metamodel for Computation (Texts in Theoretical Computer Science. An EATCS Series) by Simona Ronchi Della Rocca in Back Matter
- Komplexitätstheorie: Grenzen der Effizienz von Algorithmen (Springer-Lehrbuch) (German Edition) by Ingo Wegener in Back Matter
- A Practical Theory of Reactive Systems: Incremental Modeling of Dynamic Behaviors (Texts in Theoretical Computer Science. An EATCS Series) by R. Kurki-Suonio in Back Matter
- Process Algebra with Timing by J.C.M. Baeten in Back Matter
- Complexity Theory and Cryptology by Jörg Rothe in Back Matter
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