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The Turring Machine Captures What Computers Can Do
The turring machine looks a little bit like a toy model of computation. But actually it captures what all our real computers can do. Imagine that you have a tape and it m it extends infinitely in both directions, and it's divided into little squares. It had a tape head which could read or write a symbol on to each square of this tape. At any one time the machine is in some state. Its input is just a description of some other turring machine along with the input to that. In this way, the universal machine can do what any turring machine can do.