1 / 5

Oracles Are Subtle But Not Malicious

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 ”?

zuri
Télécharger la présentation

Oracles Are Subtle But Not Malicious

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. 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?

  3. What are you waiting for?? DOWNLOAD NOW! Web servers are standing by If you answered “yes” to any of these questions, take a look at ECCC TR05-040. • Oracle where PP has linear-size circuitsOur competitors can only promise this for MA and PNP • Oracle where PNP = P = PEXP • New proof that in the unrelativized world, PP does NOT have linear-size circuits • Bonus! PP doesn’t have linear-size quantum circuits eitherExtra Bonus: Not even quantum circuits with quantum advice

  4. 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…

More Related