Unique SAT is defined as:
Given any SAT problem, does the SAT problem have exactly 1 solution?
As I understand it is co-NPHard. I am unclear how it is in co-NP
Assuming the problem has more than 1 solution, any 2 solutions can be a certificate of it being nonUnique. That part is coNP. Now, given a problem can be unsatisfiable, how do we get a certificate of no solution?
Its also said that an NP Oracle can solve this problem in polynomial time, but an NP Oracle just tells if the problem is satisfiable. So how is that possible?
Apologies but I have no clue regarding this version of SAT.