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Published byIsaiah Gorman Modified over 2 years ago

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Oracles Are Subtle But Not Malicious Scott Aaronson (no affiliation)

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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 MA EXP ? Do you hunger for an oracle relative to which PP has linear-size circuits? Or … do you feel like its easy to construct a relativized world where anything is truelike 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 TR Oracle where PP has linear-size circuits Our competitors can only promise this for MA and P NP Oracle where P NP = P = PEXP New proof that in the unrelativized world, PP does NOT have linear-size circuits Bonus! PP doesnt have linear-size quantum circuits either Extra Bonus: Not even quantum circuits with quantum advice What are you waiting for?? DOWNLOAD NOW! Web servers are standing by

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Oracle where has linear-size circuits If P=NP, then given any Boolean function f with polynomial-size circuits, you can learn such a circuit in The implications are endless: computational learning theory (Bshouty et al.s algorithm), circuit minimization, Karp-Lipton collapses…

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