Problem Detail: Considering only the alphabet $Sigma = {0,1}$, the strings which can be given as input to the Turing machines are from the set $Sigma^{*}$. But does it make sense for the input to be an infinite binary string ? For example if a Turing machine accepts all strings starting with a 0, does a binary string of infinite zeros also belong to the language accepted by the Turing machine ?
Asked By : sashas
Answered By : Yuval Filmus
There is no problem in running a Turing machine on a tape initialized with an infinite string, although this is not usually considered. We still need the machine to terminate in finite time, though. There are also notions of infinite-time computation, which may be appropriate here.
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Question Source : http://cs.stackexchange.com/questions/48381
