Results 1  10
of
105
A Note on Genericity and BiImmunity
 In Proceedings of the Tenth Annual Structure in Complexity Theory Conference
, 1995
"... Generic sets have all properties (from among a suitably chosen class) that can be enforced by finite extension arguments. In particular, pgeneric sets are known to be Pbiimmune. We try to clarify the precise relationship between genericity and biimmunity by proposing an extended notion of biimm ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
Generic sets have all properties (from among a suitably chosen class) that can be enforced by finite extension arguments. In particular, pgeneric sets are known to be Pbiimmune. We try to clarify the precise relationship between genericity and biimmunity by proposing an extended notion of biimmunity
Biimmunity Results for Cheatable Sets
 Theoretical Computer Science
, 1995
"... An oracle A is kcheatable if there is a polynomialtime algorithm to determine the answers to 2 k parallel queries to A from the answers to only k queries to some other oracle B. It is known that 1cheatable sets cannot be biimmune for P. In contrast, we construct 2cheatable sets that are biim ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
An oracle A is kcheatable if there is a polynomialtime algorithm to determine the answers to 2 k parallel queries to A from the answers to only k queries to some other oracle B. It is known that 1cheatable sets cannot be biimmune for P. In contrast, we construct 2cheatable sets that are biimmune
Index Sets and Presentations of Complexity Classes
, 1994
"... This paper draws close connections between the ease of presenting a given complexity class C and the position of the index sets I C = f i : L(M i ) 2 C g and J C = f i : M i is total L(M i ) = 2 C g in the arithmetical hierarchy. For virtually all classes C studied in the literature, the lowest lev ..."
Abstract
 Add to MetaCart
that the classes of Pimmune and Pbiimmune languages in exponential time are not recursively presentable. It is shown that for all C with I C = 2 P 0 3 , "many" members of C do not provably (in true \Pi 2 arithmetic) belong to C. A class H is exhibited such that whether I H 2 P 0 3 is open, and I H
Calibrating randomness
 J. Symbolic Logic
"... 2. Sets, measure, and martingales 4 2.1. Sets and measure 4 2.2. Martingales 5 ..."
Abstract

Cited by 79 (34 self)
 Add to MetaCart
2. Sets, measure, and martingales 4 2.1. Sets and measure 4 2.2. Martingales 5
Almost Every Set in Exponential Time is PBiImmune
 Theoretical Computer Science
, 1994
"... . A set A is Pbiimmune if neither A nor its complement has an infinite subset in P. We investigate here the abundance of Pbiimmune languages in linearexponential time (E). We prove that the class of Pbiimmune sets has measure 1 in E. This implies that `almost' every language in E is Pbi ..."
Abstract

Cited by 57 (8 self)
 Add to MetaCart
. A set A is Pbiimmune if neither A nor its complement has an infinite subset in P. We investigate here the abundance of Pbiimmune languages in linearexponential time (E). We prove that the class of Pbiimmune sets has measure 1 in E. This implies that `almost' every language in E is Pbiimmune
Strong SelfReducibility Precludes Strong Immunity
, 1995
"... Do selfreducible sets inherently lack immunity from deterministic polynomial time? Though this is unlikely to be true in general, in this paper we prove that sufficiently strong selfreducibility precludes sufficiently strong immunity from deterministic polynomial time. In particular, we prove that ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
that NT is not P balanced immune. However, we prove that NT, a class whose sets have very strong selfreducibility properties, is P biimmune relative to a generic oracle. Thus, the previous result cannot be relativizably extended to biimmunity. We also prove that NP and \PhiP are both P balanced immune
Generalizations of the Hartmanis–Immerman–Sewelson Theorem and Applications to Infinite Subsets of PSelective Sets
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY
, 2008
"... The Hartmanis–Immerman–Sewelson theorem is the classical link between the exponential and the polynomial time realm. It states that NE = E if, and only if, every sparse set in NP lies in P. We establish similar links for classes other than sparse sets: 1. E = UE ⇐ ⇒ all functions f: {1} ∗ → Σ ∗ in ..."
Abstract
 Add to MetaCart
∀∃predicates, and show that king languages cannot be Σ p 2immune. As a consequence, /1immune and, if EΣp2 = E, not even P/1immune. Pselective sets cannot be Σ p 2 1
ResourceBounded Measure and Randomness
"... We survey recent results on resourcebounded measure and randomness in structural complexity theory. In particular, we discuss applications of these concepts to the exponential time complexity classes and . Moreover, we treat timebounded genericity and stochasticity concepts which are weaker than ..."
Abstract

Cited by 43 (6 self)
 Add to MetaCart
We survey recent results on resourcebounded measure and randomness in structural complexity theory. In particular, we discuss applications of these concepts to the exponential time complexity classes and . Moreover, we treat timebounded genericity and stochasticity concepts which are weaker than timebounded randomness but which suffice for many of the applications in complexity theory.
QueryLimited Reducibilities
, 1995
"... We study classes of sets and functions computable by algorithms that make a limited number of queries to an oracle. We distinguish between queries made in parallel (each question being independent of the answers to the others, as in a truthtable reduction) and queries made in serial (each question ..."
Abstract

Cited by 41 (14 self)
 Add to MetaCart
powerful result, the Nonspeedup Theorem, which states that 2 n parallel queries to any fixed nonrecursive oracle cannot be answered by an algorithm that makes only n queries to any oracle whatsoever. This is the tightest general result possible. A corollary is the intuitively obvious, but nontrivial
Genericity and Measure for Exponential Time
, 1994
"... . Recently Lutz [14,15] introduced a polynomial time bounded version of Lebesgue measure. He and others (see e.g. [11,13,14,15,16,17,18,20]) used this concept to investigate the quantitative structure of Exponential Time (E=DTIME (2 lin )). Previously, AmbosSpies, Fleischhack and Huwig [2,3] introd ..."
Abstract

Cited by 29 (1 self)
 Add to MetaCart
. Recently Lutz [14,15] introduced a polynomial time bounded version of Lebesgue measure. He and others (see e.g. [11,13,14,15,16,17,18,20]) used this concept to investigate the quantitative structure of Exponential Time (E=DTIME (2 lin )). Previously, AmbosSpies, Fleischhack and Huwig [2,3
Results 1  10
of
105