Title: NP Might Not Be As Easy As Detecting Unique Solutions
Authors: Richard Beigel, Harry Buhrman, and Lance Fortnow
We construct an oracle A such that
PA = PARITYPA and NPA = EXPA.
This relativized world has several amazing properties:
We also create a different relativized world where there exists a set
L in NP that is NP-complete under reductions that make one
query to L but not complete under traditional many-one
reductions. This contrasts with the result of Buhrman, Spaan and
Torenvliet showing that these two completeness notions for NEXP
- The oracle A gives the first relativized world where one can
solve satisfiability on formulae with at most one assignment yet
P ≠ NP.
- The oracle A is the first where
PA = UPA ≠ NPA = co-NPA.
- The construction gives a much simpler proof than that of Fenner,
Fortnow and Kurtz of a relativized world where all the NP-complete
sets are polynomial-time isomorphic. It is the first such computable
- Relative to A we have a collapse of
PARITYEXPA ⊆ ZPPA ⊆ PA/poly.
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