THE MYTH OF UNIVERSAL COMPUTATION ∗

It is shown that the concept of a Universal Computer cannot be realized. Speci cally, instances of a computable function F are exhibited that cannot be computed on any machine U that is capable of only a nite and xed number of operations per step. This remains true even if the machine U is endowed with an in nite memory and the ability to communicate with the outside world while it is attempting to compute F . It also remains true if, in addition, U is given an inde nite amount of time to compute F . This result applies not only to idealized models of computation, such as the Turing Machine and the like, but also to all known general-purpose computers, including existing conventional computers, as well as contemplated ones such as quantum computers.

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