Introduction to Circuit Complexity: A Uniform Approach / Edition 1

by Heribert Vollmer

Overview

This advanced textbook presents a broad and up-to-date view of the computational complexity theory of Boolean circuits. It combines the algorithmic and the computability-based approach, and includes extensive discussion of the literature to facilitate further study.

It begins with efficient Boolean circuits for problems with high practical relevance, e.g., arithmetic operations, sorting, and transitive closure, then compares the computational model of Boolean circuits with other models such as Turing machines and parallel machines. Examination of the complexity of specific problems leads to the definition of complexity classes. The theory of circuit complexity classes is then thoroughly developed, including the theory of lower bounds and advanced topics such as connections to algebraic structures and to finite model theory.

Product Details

ISBN-13:	9783540643104
Publisher:	Springer Berlin Heidelberg
Publication date:	07/30/1999
Series:	Texts in Theoretical Computer Science. An EATCS Series
Edition description:	1999
Pages:	272
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1. Complexity Measures and Reductions.- 2. Relations to Other Computation Models.- 3. Lower Bounds.- 4. The NC Hierarchy.- 5. Arithmetic Circuits.- 6. Polynomial Time and Beyond.- Appendix: Mathematical Preliminaries.- A1 Alphabets, Words, Languages.- A2 Binary Encoding.- A3 Asymptotic Behavior of Functions.- A4 Turing Machines.- A5 Logic.- A6 Graphs.- A7 Numbers and Functions.- A8 Algebraic Structures.- A9 Linear Algebra.- List of Figures.- Author Index.