Around 1936, Alan Turing conceived his model of an automated computer. This was long before the transistor was even discovered. Thus, one would think that Turing's original model could nowadays be considered a piece of computing prehistory of no other scientific interest than mere curiosity. However, at the conceptual level, Turing's model remains surprisingly up-to-date, to the extent that no scalable model of computation that has ever been physically realized has challenged its power in any essential way. In this talk I want to discuss how the most important questions around Turing's model have inspired the essentials of the modern theory of computational complexity, with the P vs NP problem at its head, followed closely by the theories of computational randomness and quantumness.
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