Lane A. Hemaspaandra, Ashish Naik, Mitsunori Ogihara, Alan L. Selman

Is there an NP function that, when given a satisfiable formula

as input, outputs one satisfying assignment uniquely? That is, can a

nondeterministic function cull just one satisfying assignment from a

possibly exponentially large collection of assignments? We show that if

there is such a nondeterministic function, then the polynomial ...
more >>>

John Hitchcock, Hadi Shafei

Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger complexity classes. We study the power of nonuniform reductions for NP-completeness, obtaining both separations and upper bounds for ... more >>>