Co-NP reduced in polynomial-time

Thread starter Dragonfall
Start date Aug 2, 2013

AI Thread Summary

Every language in co-NP can indeed be reduced in polynomial time to an instance of the formula ∀x P(x), where P is a Boolean formula with a single bound variable and no free variables. The definition of a language being in co-NP hinges on the existence of such an instance, along with the requirement that the predicate is computable in polynomial time. This highlights the relationship between co-NP languages and their polynomial-time reductions, emphasizing the computational complexity involved in verifying the properties of these languages.

Aug 2, 2013

Dragonfall

Every language in co-NP can be reduced in polynomial-time to an instance of \forall x P(x) for some Boolean formula with a single bound variable and no free variables, right?

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Aug 5, 2013

psicicle

A definition of a language being in co-NP would be that such an instance exists and the predicate is polynomial-time computable. I'm not sure if this is what you are getting at.

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