Quantitative relativizations of complexity classes
SIAM Journal on Computing
The complexity of promise problems with applications to public-key cryptography
Information and Control
Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Oracles for structural properties: the isomorphism problem and public-key cryptography
Journal of Computer and System Sciences
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
Fine hierarchies and Boolean terms
Journal of Symbolic Logic
The structural complexity of intractable search functions
The structural complexity of intractable search functions
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
Fine hierarchy of regular &ohgr;-languages
Theoretical Computer Science
A hierarchy based on output multiplicity
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
New Collapse Consequences of NP Having Small Circuits
SIAM Journal on Computing
ICCI '93 Proceedings of the Fifth International Conference on Computing and Information
On Reducibility and Symmetry of Disjoint NP-Pairs
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Cryptocomplexity and NP-Completeness
Proceedings of the 7th Colloquium on Automata, Languages and Programming
New Collapse Consequences of NP Having Small Circuits
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Separability and One-Way Functions
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
Computing Solutions Uniquely collapses the Polynomial Hierarchy
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
Two Refinements of the Polynomial Hierarcht
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Equivalence relations, invariants, and normal forms
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Optimal proof systems imply complete sets for promise classes
Information and Computation
Information and Computation
Separability and one-way functions
Computational Complexity
SIAM Journal on Computing
Reductions between disjoint NP-Pairs
Information and Computation
Fine hierarchy of regular aperiodic ω-languages
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Inverting onto functions and polynomial hierarchy
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Complexity classes of equivalence problems revisited
Information and Computation
Hi-index | 5.23 |
We study the shrinking and separation properties (two notions well-known in descriptive set theory) for NP and coNP and show that under reasonable complexity-theoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain the following results. 1.NP and coNP do not have the shrinking property unless PH is finite. In general, @S"n^P and @P"n^P do not have the shrinking property unless PH is finite. This solves an open question posed by Selivanov (1994) [33]. 2.The separation property does not hold for NP unless UP@?coNP. 3.The shrinking property does not hold for NP unless there exist NP-hard disjoint NP-pairs (existence of such pairs would contradict a conjecture of Even et al. (1984) [6]). 4.The shrinking property does not hold for NP unless there exist complete disjoint NP-pairs. Moreover, we prove that the assumption NPcoNP is too weak to refute the shrinking property for NP in a relativizable way. For this we construct an oracle relative to which P=NP@?coNP, NPcoNP, and NP has the shrinking property. This solves an open question posed by Blass and Gurevich (1984) [3] who explicitly ask for such an oracle.