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 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?

3. If you answered yes to any of these questions, take a look at ECCC TR05-040. 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

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…