Abstract
For every recursive set A, let PP-A denote the following promise problem. input x and y promise (x∈A)⊕(y∈A) property x∈A. We show that if L is a solution of PP-A, then A∈PL/Poly. From this result, it follows that if A is ≤ PT -hard for NP, then all solutions of PP-A are hard for NP under a reduction that generalizes both ≤ PT and ≤ SNT . Specifically, if A is NP-hard, then all solutions of PP-A are generalized high 2. [BBS86b]. The main theorem that leads to this result states that if B is a self- reducible set, B≤ PT A, and A∈PL/Poly, then Σ P,B2 ...Σ P,L2 . Several interesting connections between uniform and nonuniform complexity follow directly from this theorem.
Funding for this research was provided by the National Security Agency under grant MDA-87-H-2020
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Longpré, L., Selman, A.L. (1990). Hard promise problems and nonuniform complexity. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_45
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DOI: https://doi.org/10.1007/3-540-52282-4_45
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