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REPORTS > KEYWORD > KARP-LIPTON THEOREMS:
Reports tagged with Karp-Lipton theorems:
TR16-197 | 7th December 2016
Igor Carboni Oliveira, Rahul Santhanam

Conspiracies between Learning Algorithms, Circuit Lower Bounds and Pseudorandomness

We prove several results giving new and stronger connections between learning theory, circuit complexity and pseudorandomness. Let C be any typical class of Boolean circuits, and C[s(n)] denote n-variable C-circuits of size at most s(n). We show:

Learning Speedups: If C[$n^{O(1)}$] admits a randomized weak learning algorithm under the uniform ... more >>>


TR24-052 | 15th March 2024
Justin Yirka

Even quantum advice is unlikely to solve PP

Revisions: 1

We give a corrected proof that if PP $\subseteq$ BQP/qpoly, then the Counting Hierarchy collapses, as originally claimed by [Aaronson, CCC 2006]. This recovers the related unconditional claim that PP does not have circuits of any fixed size $n^k$ even with quantum advice. We do so by proving that YQP*, ... more >>>




ISSN 1433-8092 | Imprint