Theory of Semi-Feasible Algorithms / Edition 1

by Lane A. Hemaspaandra, Leen Torenvliet

Overview

An Invitation to the Dance It is an underappreciated fact that sets may have various types of complexity, and not all types are in harmony with each other. The primary goal of this book is to unify and make more widely accessible a vibrant stream of research-the theory of semi-feasible computation-that perfectly showcases the richness of, and contrasts between, the central types of complexity. The semi-feasible sets, which are most commonly referred to as the P­ selective sets, are those sets L for which there is a deterministic polynornial­ time algorithm that, when given as input any two strings of which at least one belongs to L, will output one of them that is in L. The reason we saythat the semi-feasible sets showcase the contrasts among types of complexity is that it is well-known that many semi-feasible sets have no recursive algorithms (thus their time complexitycannot be upper-bounded by standard time-complexity classes), yet all semi-feasible sets are simple in a wide range of other natural senses. In particular, the semi-feasible sets have small circuits, they are in the extended low hierarchy, and they cannot be NP-complete unless P = NP. The semi-feasible sets are fascinating for many reasons. First, as mentioned above, they showcase the fact that mere deterministic time complexity is not the only potential type of complexity in the world of computation.

Product Details

ISBN-13:	9783642075810
Publisher:	Springer Berlin Heidelberg
Publication date:	12/08/2010
Series:	Monographs in Theoretical Computer Science. An EATCS Series
Edition description:	Softcover reprint of the original 1st ed. 2003
Pages:	150
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

1. Introduction to Semi-Feasible Computation.- 2. Advice.- 3. Lowness.- 4. Hardness for Complexity Classes.- 5. Closures.- 6. Generalizations and Related Notions.- A. Definitions of Reductions and Complexity Classes, and Notation List.- A.1 Reductions.- A.2 Complexity Classes.- A.3 Some Other Notation.- References.

Editorial Reviews

From the reviews:

"This book focuses mainly on the complexity of P-selective sets … . a course from this text would require a highly-motivated instructor who can give the intuitive ideas leaving the details to the book. The book would also serve as a reasonable reference for those doing research in this area." (Lance Fortnow, SIGACT News, Vol. 35 (2), 2004)

From the Publisher