Oracles Are Subtle But Not Malicious. Scott Aaronson (no affiliation). Are you frustrated by the scarcity of nonrelativizing circuit lower bounds? Dissatisfied by results that apply only to made-up classes like “MA EXP ”?
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Are you frustrated by the scarcity of nonrelativizing circuit lower bounds?
Dissatisfied by results that apply only to made-up classes like “MAEXP”?
Do you hunger for an oracle relative to which PP has linear-size circuits?
Or … do you feel like it’s easy to construct a relativized world where anything is true—like you never get more out of oracle results than you put in to them?
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If you answered “yes” to any of these questions, take a look at ECCC TR05-040.
The implications are endless: computational learning theory (Bshouty et al.’s algorithm), circuit minimization, Karp-Lipton collapses…