Considering only the alphabet Σ={0,1}, the strings which can be given as input to the Turing machines are from the set Σ∗. 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 ?

**Answer**

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.

**Attribution***Source : Link , Question Author : sashas , Answer Author : Yuval Filmus*