Turing test not merely "simulation of human conversational behaviour". The general structure of the OIG test could even be used with non-verbal versions of imitation games. Still other writers have interpreted Turing as proposing that the imitation game itself is the test, without specifying how to take into account Turing's statement that the test that he proposed using the party version of the imitation game is based upon a criterion of comparative frequency of success in that imitation game, rather than a capacity to succeed at one round of the game. Saygin has suggested that maybe the original game is a way
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.