" polynomial complexity theory extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems.Expand

UNIFORM COMPLEXITY. Models of Computation and Complexity Classes. NP-Completeness. The Polynomial-Time Hierarchy and Polynomial Space. Structure of NP. NONUNIFORM COMPLEXITY. Decision Trees. Circuit… Expand

It is proved that self-reducible sets are not polynomial-time Turing reducible to these sets, and weakly p -selective sets are introduced as a generalization of p - selective sets based on this characterization.Expand

The computational complexity of optimization problems of the min-max form is naturally characterized by ∏ 2 P , the second level of the polynomial-time hierarchy. We present a number of optimization… Expand

The oracle Turing machine is introduced as the formal model for computing real functions and the class of polynomial time computable real functions is defined, and several characterizations of this class will be given.Expand

This book organizes approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader and teacher can study approximation algorithms of the same nature together.Expand

The concept of helping by robust oracle Turing machines is extended to the notion of ‘one-sided helping’ and its relations to the structural properties of NP sets are investigated.Expand

This work investigates several natural operators which share similar properties and uses the concept of completeness to give a precise classification of the complexity of these operators.Expand

It is shown that the first two definitions of infinite pseudorandom sequences are equivalent with respect to polynomial space complexity, while both are strictly stronger than the third definition, which is derived from Von Mises's notion of collectives.Expand