Buch, Englisch, 160 Seiten, Paperback, Format (B × H): 210 mm x 279 mm, Gewicht: 436 g
Its Structural Complexity
Buch, Englisch, 160 Seiten, Paperback, Format (B × H): 210 mm x 279 mm, Gewicht: 436 g
Reihe: Progress in Theoretical Computer Science
ISBN: 978-1-4612-6712-6
Verlag: Birkhäuser Boston
Recently, a variety ofresults on the complexitystatusofthegraph isomorphism problem has been obtained. These results belong to the so-called structural part of Complexity Theory. Our idea behind this book is to summarize such results which might otherwise not be easily accessible in the literature, and also, to give the reader an understanding of the aims and topics in Structural Complexity Theory, in general. The text is basically self contained; the only prerequisite for reading it is some elementary knowledge from Complexity Theory and Probability Theory. It can be used to teach a seminar or a monographic graduate course, but also parts of it (especially Chapter 1) provide a source of examples for a standard graduate course on Complexity Theory. Many people have helped us in different ways III the process of writing this book. Especially, we would like to thank V. Arvind, R.V. Book, E. May ordomo, and the referee who gave very constructive comments. This book project was especially made possible by a DAAD grant in the "Acciones In tegrada" program. The third author has been supported by the ESPRIT project ALCOM-II.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
- Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
Weitere Infos & Material
Preliminaries.- 1 Decision Problems, Search Problems, and Counting Problems.- 1.1 NP-Completeness.- 1.2 Reducing the Construction Problem to the Decision Problem.- 1.3 Counting versus Deciding for Graph Isomorphism.- 1.4 Uniqueness of the Solution.- 1.5 Reducing Multiple Questions to One.- 2 Quantifiers, Games, and Interactive Proofs.- 2.1 The Polynomial-Time Hierarchy.- 2.2 Interactive Proof Systems.- 2.3 Probabilistic Classes.- 2.4 Lowness and Collapses.- 3 Circuits and Sparse Sets.- 3.1 Polynomial Size Circuits.- 3.2 Reductions to Sparse Sets.- 4 Counting Properties.- 4.1 Decision Reduces to Parity.- 4.2 Graph Isomorphism is Low for PP.- 4.3 The Reconstruction Conjecture.
