Turing test arisen over which of the alternative formulations of the test Turing intended. Sterrett argues that two distinct tests can be extracted from his 1950 paper and that, "pace" Turing's remark, they are not equivalent. The test that employs the party game and compares frequencies of success is referred to as the "Original Imitation Game Test", whereas the test consisting of a human judge conversing with a human and a machine is referred to as the "Standard Turing Test", noting that Sterrett equates this with the "standard interpretation" rather than the second version of the imitation game. Sterrett agrees that the
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.