A comparison of polynomial time completeness notions
Theoretical Computer Science
Strong nondeterministic turing reduction—a technique for proving intractability
Journal of Computer and System Sciences
Complete problems and strong polynomial reducibilities
SIAM Journal on Computing
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Cook versus Karp-Levin: separating completeness notions if NP is not small
Theoretical Computer Science
Resource bounded randomness and weakly complete problems
Theoretical Computer Science
NP-hard sets are superterse unless NP is small
Information Processing Letters
Structural properties of complete problems for exponential time
Complexity theory retrospective II
The quantitative structure of exponential time
Complexity theory retrospective II
Reductions in circuit complexity: an isomorphism theorem and a gap theorem
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Separating NP-Completeness notions under strong Hypotheses
Journal of Computer and System Sciences
Twelve problems in resource-bounded measure
Current trends in theoretical computer science
Reducing the complexity of reductions
Computational Complexity
Compressibility and Resource Bounded Measure
SIAM Journal on Computing
Separation of NP-Completeness Notions
SIAM Journal on Computing
Reducibility, randomness, and intractibility (Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Pseudo-Random Generators and Structure of Complete Degrees
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Polynomial reducibilities and complete sets.
Polynomial reducibilities and complete sets.
The cpa's responsibility for the prevention and detection of computer fraud.
The cpa's responsibility for the prevention and detection of computer fraud.
Information and Computation
Bi-immunity separates strong NP-completeness notions
Information and Computation
Partial Bi-immunity, Scaled Dimension, and NP-Completeness
Theory of Computing Systems
Hardness hypotheses, derandomization, and circuit complexity
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
The complexity of unions of disjoint sets
Journal of Computer and System Sciences
The complexity of unions of disjoint sets
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A thirty year old conjecture about promise problems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Under the assumption that NP does not have p-measure 0, we investigate reductions to NP-complete sets and prove the following: Adaptive reductions are more powerful than nonadaptive reductions: there is a problem that is Turing-complete for NP but not truth-table-complete. Strong nondeterministic reductions are more powerful than deterministic reductions: there is a problem that is SNP-complete for NP but not Turing-complete. Every problem that is many-one complete for NP is complete under length-increasing reductions that are computed by polynomial-size circuits. The first item solves one of Lutz and Mayordomo's “Twelve Problems in Resource-Bounded Measure” (1999). We also show that every problem that is complete for NE is complete under one-to-one, length-increasing reductions that are computed by polynomial-size circuits.