We show that if the Boolean hierarchy collapses to level k, then the polynomial hierarchy collapses to BH3(k), where BH3(k) is the kth level of the Boolean hierarchy over P 2 . Th...
The general dimension is a combinatorial measure that characterizes the number of queries needed to learn a concept class. We use this notion to show that any p-evaluatable concep...
Abstract. Often, qualitative values have an ordering, such as (veryshort, short, medium-height, tall) or a hierarchical level, such as (TheWorld, Europe, Spain, Madrid), which are ...
Kadin [6] showed that if the Polynomial Hierarchy (PH) has infinitely many levels, then for all k, PSAT[k] ⊂ PSAT[k+1]. This paper extends Kadin’s technique and shows that a p...