Nonuniform proof systems: a new framework to describe nonuniform and probabilistic complexity classes

Random languages for nonuniform complexity classes

A language A is considered to be random for a class C if for every language B in C the fraction of the strings where A and B coincide is approximately 1/2. We show that there exist languages in DSPACE(f(n)) which are random for the non-uniform class DSPACE(g(n))=h(n), where n, g(n) and h(n) are in o(f(n)). Non-uniform complexity classes were introduced by Karp and Lipton Karp and Lipton 1980] a...

Nonuniform Complexity Classes Specified by Lower and Upper Bounds

We characterize in terms of oracle Turing machines the classes defined by exponential lower bounds on some nonuniform complexity measures. After, we use the same methods to giue a new characterization of classes defined by polynomial and polylog upper bounds, obtaining an unified approach to deal with upper and lower bounds, The main measures are the initial index, the context-free cosU ond the...

Nonuniform Hard Boolean Functions and Uniform Complexity Classes

Separating NE from Some Nonuniform Nondeterministic Complexity Classes

We investigate the question whether NE can be separated from the reduction closures of tally sets, sparse sets and NP. We show that (1) NE ⊆ RNP no(1)−T (TALLY); (2) NE ⊆ R m (SPARSE); (3) NEXP ⊆ PNP nk−T /n for all k ≥ 1; and (4) NE ⊆ Pbtt (NP ⊕ SPARSE). Result (3) extends a previous result by Mocas to nonuniform reductions. We also investigate how different an NE-hard set is from an NP-set. W...

Scaled Dimension and Nonuniform Complexity

Resource-bounded dimension is a complexity-theoretic extension of classical Hausdorff dimension introduced by Lutz (2000) in order to investigate the fractal structure of sets that have resource-bounded measure 0. For example, while it has long been known that the Boolean circuit-size complexity class SIZE ( α n