How am I supposed to read the P=?NP relativization proof? I am reading

Theodore Baker, John Gill, and Robert Solovay. Relativization of the P=?NP problem. Siam Journal of Computing, 4:432-442, 1975 [219]

in particular the proof that there exist an oracle B such that P^B = NP^B on page 436. I have some questions and your help will be appreciated.

  • The procedure does not seem to be an oracle but a deterministic algorithm ... ?

  • Is this construction a counterexample to P = NP?

  • What does this mean "Run query machine P_i with oracle B_i on input x_i = 0^n?" Does it mean that P_i asks

a) if B_i accepts 0^n

b) if B_i accepts any string of lenght n

c) ONE BY ONE if B_i accepts a string of length n from the canonical enumeration?

  • I assume that the set B or B_i is initially empty. Does it mean that the FIRST string of length n form the canonical enumeration will always be added?




closed as off-topic by Emil Jeřábek, Gamow, Jan Johannsen, D.W., Sasho Nikolov Sep 9 at 18:09

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