Theory of Semi-Feasible Algorithms

1. Front Matter

   Pages i-x

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2. Introduction to Semi-Feasible Computation

   • Lane A. Hemaspaandra, Leen Torenvliet

   Pages 1-16

3. Advice

   • Lane A. Hemaspaandra, Leen Torenvliet

   Pages 17-40

4. Lowness

   • Lane A. Hemaspaandra, Leen Torenvliet

   Pages 41-59

5. Hardness for Complexity Classes

   • Lane A. Hemaspaandra, Leen Torenvliet

   Pages 61-78

6. Closures

   • Lane A. Hemaspaandra, Leen Torenvliet

   Pages 79-103

7. Generalizations and Related Notions

   • Lane A. Hemaspaandra, Leen Torenvliet

   Pages 105-113

8. Back Matter

   Pages 115-149

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An Invitation to the Dance It is an underappreciated fact that sets may have various types of complex­ ity, 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 men­ tioned above, they showcase the fact that mere deterministic time complex­ ity is not the only potential type of complexity in the world of computation.

• Algorithms
• Circuits
• Complexity
• Computer
• Discrete Mathematics
• complexity theory
• computer science
• semi-feasible algorithms
• algorithm analysis and problem complexity
• combinatorics

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)

• Department of Computer Science, University of Rochester, Rochester, USA

  Lane A. Hemaspaandra

• Department of Computer Science, University of Amsterdam, Amsterdam, The Netherlands

  Leen Torenvliet

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