# $\overline{SAT}$ vs. $UNSAT$, Is it the same?

I know this question may look stupid, but still..
Is the meaning of both "have no satisfiable assignment"?

## 1 Answer

They are not precisely the same language. For instance, $$\overline{SAT}$$ has words that are not even formulas. $$UNSAT$$ on the other hand, has only formulas that are not satisfiable.

In terms of complexity measures - the two languages are equivalent, since we can check in polynomial time whether a given input word is a formula or not and therefore we have a poly-time reduction from $$\overline{SAT}$$ to $$UNSAT$$ and vice versa.

• Thanks man! great answer, simple and clear!! – ChaosPredictor Feb 10 at 15:32