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Alan Turing proposed an interactive test to replace the question "Can machines think?" This test has become known as the Turing Test and its validity for determining intelligence or thinking is still in question.Struggling with the validity of long proofs, program correctness, computational complexity and cryptography, theoreticians developed interactive proof systems. By formalizing the Turing Test as an interactive proof system and by employing results from complexity theory, this paper investigates the power and limitations of the Turing Test. In particular, assuming the notion of completeness for standard complexity classes carries over faithfully to human cognition, then we can say: if human intelligence subsumes machine intelligence, and human intelligence is not simulatable by any bounded machine, then the Turing Test can distinguish humans and machines to within arbitrarily high probability.This paper makes no claim about the Turing Test's sufficiency to distinguish humans and machines. Rather, through its formalization this paper gives several ramifications involving the acceptance or rejection of the Turing Test as sufficient for making any such distinction.

A formalization of the Turing test