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Learning algorithms versus automatability of Frege systems
If there is a function $h\in NE\cap coNE$ which is hard on average for circuits of size $2^{n/4}$, for each sufficiently big $n$, then there is an explicit propositional proof system $P$ satisfying properties I.-III., i. e. the equivalence of Items 1 and 2 holds for $P$.
Conspiracies between Learning Algorithms, Circuit Lower Bounds and Pseudorandomness
We prove several results giving new and stronger connections between learning, circuit lower bounds and pseudorandomness.
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