On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Reducibility, randomness, and intractibility (Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Riemann's Hypothesis and tests for primality
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Computational complexity of probabilistic Turing machines
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Relativized Questions Involving Probabilistic Algorithms
Journal of the ACM (JACM)
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Let R @@@@ NP be the collection of languages L such that for some polynomial time computable predicate P(x,y) and constant k, L &equil; {x|@@@@y, |y|&equil;|x|k,P(x,y)} &equil; {x|@@@@ at least 2|x|k−1 values of y, |y|&equil;|x|k,P(x,y)}. Let U @@@@ NP be the collection of languages L such that for some polynomial time computable predicate P(x,y) and constant k, L &equil; {x|@@@@y,|y|&equil;|x|k,P(x,y)}&equil; {x|@@@@ unique y, |y|&equil;|x|k,p(x,y)}. Let RA,UA, PA,NPA,CO-NPA be the relativization of these classes with respect to an oracle A as in [ 5 ]. Then for some oracle E (NPE @@@@ CO-NPE) &equil; UE &equil; RE &equil; PE @@@@ NPE while for some other oracle D CO-NPD &equil; NPD &equil; UD &equil; RD @@@@ PD.