Immunity, relativizations, and nondeterminism
SIAM Journal on Computing
On helping by robust oracle machines
Theoretical Computer Science
A comparison of polynomial time completeness notions
Theoretical Computer Science
Promises and fault-tolerant database access
Complexity theory
P-selectivity: intersections and indices
Theoretical Computer Science
Threshold Computation and Cryptographic Security
SIAM Journal on Computing
Structural properties of complete problems for exponential time
Complexity theory retrospective II
SIAM Journal on Computing
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Separating NP-Completeness notions under strong Hypotheses
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Separation of NP-Completeness Notions
SIAM Journal on Computing
FCT '85 Fundamentals of Computation Theory
P-immune sets with holes lack self-reducibility properties
Theoretical Computer Science
One-way permutations and self-witnessing languages
Journal of Computer and System Sciences
General tools for determining problem complexity
General tools for determining problem complexity
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
Query-monotonic turing reductions
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Autoreducibility, mitoticity, and immunity
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Hi-index | 5.23 |
We study reductions that limit the extreme adaptivity of Turing reductions. In particular, we study reductions that make a rapid, structured progression through the set to which they are reducing: Each query is strictly longer (shorter) than the previous one. We call these reductions query-increasing (query-decreasing) Turing reductions. We also study query-nonincreasing (query-nondecreasing) Turing reductions. These are Turing reductions in which the sequence of query lengths is nonincreasing (nondecreasing). We ask whether these restrictions in fact limit the power of reductions. We prove that query-increasing and query-decreasing Turing reductions are incomparable with (that is, are neither strictly stronger than nor strictly weaker than) truth-table reductions and are strictly weaker than Turing reductions. In addition, we prove that query-nonincreasing and query-nondecreasing Turing reductions are strictly stronger than truth-table reductions and strictly weaker than Turing reductions. Despite the fact that we prove query-increasing and query-decreasing Turing reductions to in the general case be strictly weaker than Turing reductions, we identify a broad class of sets A for which any set that Turing reduces to A will also reduce to A via both query-increasing and query-decreasing Turing reductions. In particular, this holds for all tight paddable sets, where a set is said to be tight paddable exactly if it is paddable via a function whose output length is bounded tightly both from above and from below in the length of the input. We prove that many natural NP-complete problems such as satisfiability, clique, and vertex cover are tight paddable.