The Boolean hierarchy is generalized in such a way that it is possible to characterize P and O in terms of the generalization, and the class $P^{\text{NP}}[O(\log n)]$ can be characterized in very different ways.Expand

It is shown that problems defined by more complicated questions about maxima and minima are complete in certain subclasses of the Boolean closure of NP and other classes in the interesting area below the class Δ p 2 of the polynomial-time hierarchy.Expand

It turns out that some of the languages investigated for the succinct representation of the instances of combinatorial problems are not comparable, unless P=NP Some problems left open in [2].Expand

The complexity of sets formed by boolean operations (union, intersection, and complement) on NP sets are studied, showing that in some relativized worlds the boolean hierarchy is infinite, and that for every k there is a relativization world in which the Boolean hierarchy extends exactly k levels.Expand

The problem of testing membership in the subset of the natural numbers produced at the output gate of a combinational circuit is shown to capture a wide range of complexity classes, and results extend in nontrivial ways past work by Stockmeyer and Meyer, Wagner, Wagner and Yang.Expand

A hierarchical graph model is discussed that allows to exploit the hierarchical description of the graphs for the efficient solution of graph problems.Expand

The question of how complex a leaf language must be in order to characterize some given class C is investigated, which leads to the examination of the closure of different language classes under bit-reducibility.Expand

It turns out that further natural subclasses of the class of ω-regular sets coincide or are at least comparable to each other in terms of structural complexity, topological difficulty, and m-reducibility with finite automata.Expand