Turing test B being taken by a man? In this version, both player A (the computer) and player B are trying to trick the interrogator into making an incorrect decision. Common understanding has it that the purpose of the Turing test is not specifically to determine whether a computer is able to fool an interrogator into believing that it is a human, but rather whether a computer could "imitate" a human. While there is some dispute whether this interpretation was intended by Turing, Sterrett believes that it was and thus conflates the second version with this one, while others, such as Traiger,
Church–Turing thesis three formally-defined classes of computable functions coincide with the "informal" notion of an effectively calculable function. Since, as an informal notion, the concept of effective calculability does not have a formal definition, the thesis, although it has near-universal acceptance, cannot be formally proven. Since its inception, variations on the original thesis have arisen, including statements about what can physically be realized by a computer in our universe (physical Church-Turing thesis) and what can be efficiently computed (Church–Turing thesis (complexity theory)). These variations are not due to Church or Turing, but arise from later work in complexity theory and digital physics.