Relating Partial and Complete Solutions and the Complexity of Computing Smallest Solutions
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
Polynomial reducibilities and upward diagonalizations
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Information and Computation
Separability and one-way functions
Computational Complexity
On computing the smallest four-coloring of planar graphs and non-self-reducible sets in P
Information Processing Letters
Structural complexity of multiobjective NP search problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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In Valiant [11] and Schnorr [9], concepts of "functional self-reducibility" are introduced and investigated. We concentrate on the class NP and on the NP hierarchy of Meyer and Stockmeyer [7] to further investigate these ideas. Assuming that the NP hierarchy exists (specifically, assuming that $P \stackrel{\subset}{+} NP = \sum^{P}_{1} \stackrel{\subset}{+} \sum^{P}_{2}$ we show that, while every complete set in $\sum^{P}_{2}$ is functionally self-reducible, there exist sets in $\sum^{P}_{2}$ which are not functionally self-reducible.