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Complexity Theory Retrospective II

Complexity Theory Retrospective II


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About the Book

Complexity theory has been a flourishing area of research in the last ten years and currently provides one of the most active subjects for future research problems in computer science. This volume provides a survey of the subject in the form of a collection of articles written by experts that to- gether provide a comprehensive guide to research. The editors' aim has been to provide an accessible description of the current state of complexity theory,and to demonstrate the breadth of techniques and results that make the subject exciting. Thus, papers run the gamut from sublogarithmic space to exponential time and from new combinatorial techniques to interactive proof systems. As a result, researchers in computer science will find this an excellent starting point for study in the subject and a useful source of the key results known.

Table of Contents:
1 Time, Hardware, and Uniformity.- 1 Introduction.- 2 Background: Descriptive Complexity.- 3 First Uniformity Theorem.- 4 Variables That Are Longer Than log nBits.- 5 Uniformity: The Third Dimension.- 6 Variables That Are Shorter Than log nBits.- 7 Conclusions.- 2 Quantum Computation.- 1 The Need for Quantum Mechanics.- 2 Basic Principles of Quantum Mechanics.- 3 Computing with Quantum Registers.- 4 Separating Two Classes of Functions.- 5 Shor’s Factoring Algorithm.- 6 Building a Quantum Computer.- 3 Sparse Sets versus Complexity Classes.- 1 Introduction.- 2 Earlier Results for Turing Reductions.- 3 Earlier Results for Many-One Reductions.- 4 Bounded Truth Table Reduction of NP.- 5 The Hartmanis Conjecture for P.- 6 Conclusions.- 4 Counting Complexity.- 1 Introduction.- 2 Preliminaries.- 3 Counting Functions.- 4 Counting Classes.- 5 Relativization.- 6 Other Work.- 5 A Taxonomy of Proof Systems.- 1 Introduction.- 2 A Technical Exposition.- 3 The Story.- 6 Structural Properties of Complete Problems for Exponential Time.- 1 Introduction.- 2 Strong Reductions to Complete Sets.- 3 Immunity for Complete Problems.- 4 Differences between Complete Sets.- 5 Other Properties and Open Problems.- 7 The Complexity of Obtaining Solutions for Problems in NP and NL.- 1 Introduction.- 2 Computing Optimal Solutions: The Class FPNP.- 3 Bounded Queries to NP.- 4 Computing Solutions Uniquely: The Class NPSV.- 5 Nonadaptive Queries to NP: The Class FPNPtt.- 6 A Look inside Nondeterministic Logspace.- 7 Conclusions.- 8 Biological Computing.- 1 Introduction.- 2 The One-Molecule Processor.- 3 A Brief Introduction to Biochemistry.- 4 Computational Molecules.- 5 The Microarchitecture of CNA Computers.- 6 A Brief Discussion of Adleman’s Model Versus Our Model.- 7 Conclusions.- 9 Computing withSublogarithmic Space.- 1 Are Sublogarithmic Space Classes of Any Interest?.- 2 The Alternating Sublogarithmic Space World.- 3 Adding Randomness.- 4 Special Limitations of Machines with a Sublogarithmic Space Bound.- 5 A Survey of Lower Space Bound Proofs.- 6 Conclusions and Open Problems.- 10 The Quantitative Structure of Exponential Time.- 1 Introduction.- 2 Preliminaries.- 3 Resource-Bounded Measure.- 4 Incompressibility and Bi-Immunity.- 5 Complexity Cores.- 6 Small Span Theorems.- 7 Weakly Hard Problems.- 8 Upper Bounds for Hard Problems.- 9 Nonuniform Complexity, Natural Proofs, and Pseudorandom Generators.- 10 Weak Stochasticity.- 11 Density of Hard Languages.- 12 Strong Hypotheses.- 13 Conclusions and Open Directions.- 11 Polynomials and Combinatorial Definitions of Languages.- 1 Introduction.- 2 Polynomials.- 3 Representation Schemes and Language Classes.- 4 Strong versus Weak Representation.- 5 Known Upper and Lower Bounds on Degree.- 6 Polynomials for Closure Properties.- 7 Probabilistic Polynomials.- 8 Other Combinatorial Structures.- 12 Average-Case Computational Complexity Theory.- 1 Introduction.- 2 Average Polynomial Time.- 3 Average-Case Completeness.- 4 Randomization.- 5 Hierarchies of Average-Case Complexity.- 6 A Brief Survey of Other Results.


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Product Details
  • ISBN-13: 9780387949734
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Height: 235 mm
  • No of Pages: 339
  • Returnable: Y
  • ISBN-10: 0387949739
  • Publisher Date: 05 Jun 1997
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Width: 155 mm


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