On boolean lowness and boolean highness

On Boolean Lowness and Boolean Highness

The concepts of lowness and highness originate from recursion theory and were introduced into the complexity theory by Sch. oning (Lecture Notes in Computer Science, Vol. 211, Springer, Berlin, 1985). Informally, a set is low (high resp.) for a relativizable class K of languages if it does not add (adds maximal resp.) power to K when used as an oracle. In this paper, we introduce the notions of...

Sparse Oracles, Lowness, and Highness

The polynomial-time hierarchy has been studied extensively since it lies between the class P of languages accepted deterministically in polynomial time and the class PSPACE of languages accepted (deterministically or nondeterministically) in polynomial space. Since the P =? NP problem is still unsolved, it is not known whether the hierarchy is nontrivial, although it is known that there is a re...

Polynomial Depth, Highness and Lowness for E

We study the relations between the notions of highness, lowness and logical depth in the setting of complexity theory. We introduce a new notion of polynomial depth based on time bounded Kolmogorov complexity. We show our polynomial depth notion satisfies all basic logical depth properties, namely neither sets in P nor sets random for EXP are polynomial deep, and only polynomial deep sets can p...

Omega-almost Boolean rings

In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.

Generalized Lowness and Highness and Probabilisti Complexity Classes