A formalization of the Turing test

Abstract

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.

The Turing Test as Interactive Proof

“…6 Hobbs, Stickel, Martin, and Edwards (1988) present a similar symmetrical view of the three types of reasoning. 7 In independent work, Bradford and Wollowski (1994) do attempt to provide a mathematical argument relating interactive proofs and the Turing Test, but of a quite different flavor. For instance, they assume that the subject-under-test is polynomially bounded, and take the subject-under-test and confederate to be the verifiers, and the judge to be the prover.…”

Turing Test as a Defining Feature of AI-Completeness

“…In this section we will show that a Turing Test [50] [45,8,44]. Second requirement for a problem to be proven to be AI-Complete is that any other AI problem should be convertible into an instance of the problem under consideration in polynomial time via Turing reduction.…”

A formal approach to exploring\\ the interrogator's perspective in the Turing test

“…The e-scenario for our exemplary problem, written in language L, is presented in the schema (2). D-wffs are either answers to auxiliary questions or are entailed by preceding d-wffs.…”

“…This kind of an approach to the TT is not very popular in the literature, but there are papers worth to be mention here, like: [19] (Turing Machines approach), [9] (exploring computational complexity for the Turing test setting), [2,23,22] within Inferential Erotetic Logic, so called erotetic search scenarios (escenarios for short). First, I reconstruct the setting of the Turing test proposed by A. M. Turing.…”