Automata and Computability

Describe the error in the following fallacious "proof" that P  NP. Consider an algorithm for SAT: "On input , try all possible assignments to the variables. Accept if any satisfy ." This algorithm clearly requires exponential time. Thus SAT has exponential time complexity. Therefore SAT is not in P. Because SAT is in NP, it must be true that P is not equal to NP.

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