On Boolean Lowness and Boolean Highness
نویسندگان
چکیده
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 boolean lowness and boolean highness. Informally, a set is boolean low (boolean high resp.) for a class K of languages if it does not add (adds maximal resp.) power to K when combined with K by boolean operations. We prove properties of boolean lowness and boolean highness which show a lot of similarities with the notions of lowness and highness. Using Kadin’s technique of hard strings (see Kadin, SIAM J. Comput 17(6) (1988) 1263–1282; Wagner, Number-of-query hierachies, TR 158, University of Augsburg, 1987; Chang and Kadin SIAM J. Comput. 25(2) (1996) 340; Beigel et al. Math. Systems Theory 26 (1993) 293–310) we show that the sets which are boolean low for the classes of the boolean hierarchy are low for the boolean closure of p 2 . Furthermore, we prove a result on boolean lowness which has as a corollary the best known result (see Beigel, (1993); in fact even a bit better) on the connection of the collapses of the boolean hierarchy and the polynomial-time hierarchy if BH = NP(k) then PH = p 2 (k − 1)⊕ NP(k). c © 2001 Published by Elsevier Science B.V.
منابع مشابه
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...
متن کاملFilter theory in MTL-algebras based on Uni-soft property
The notion of (Boolean) uni-soft filters in MTL-algebras is introduced, and several properties of them are investigated. Characterizations of (Boolean) uni-soft filters are discussed, and some (necessary and sufficient) conditions for a uni-soft filter to be Boolean are provided. The condensational property for a Boolean uni-soft filter is established.
متن کاملω-Change Randomness and Weak Demuth Randomness
We extend our work on difference randomness. Each component of a difference test is a Boolean combination of two r.e. open sets; here we consider tests in which the k component is a Boolean combination of g(k) r.e. open sets for a given recursive function g. We use this method to produce an alternate characterization of weak Demuth randomness in terms of these tests and further show that a real...
متن کاملOmega-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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 261 شماره
صفحات -
تاریخ انتشار 1998