If you replace Riemann hypothesis by “any provable mathematical statement” and you allow arbitrary verification procedures instead of just the normal mathematical ones, then the question is probably equivalent to P = coNP, which is equivalent to P = NP.
I assume you’re thinking of this—P=coNP ⇒ polytime decision for propositional tautologies (but not for mixed quanitifier bool. formulas). It’s CoNP-complete to decide tautologies (implicit forall for all the prop. vars) and NP-complete to decide satisfiability (implicit exists for all the prop. vars).
I don’t understand what you mean by “arbitrary verification procedures”—maybe you’re talking about a different result than the one I linked above?
If you replace Riemann hypothesis by “any provable mathematical statement” and you allow arbitrary verification procedures instead of just the normal mathematical ones, then the question is probably equivalent to P = coNP, which is equivalent to P = NP.
I assume you’re thinking of this—P=coNP ⇒ polytime decision for propositional tautologies (but not for mixed quanitifier bool. formulas). It’s CoNP-complete to decide tautologies (implicit forall for all the prop. vars) and NP-complete to decide satisfiability (implicit exists for all the prop. vars).
I don’t understand what you mean by “arbitrary verification procedures”—maybe you’re talking about a different result than the one I linked above?
Right—those are equivalent.