How to construct a single-tape Turing Machine which writes the number 7 in UNARY number system, leaving the tape with a delimiter symbol followed by 7 1s?

So outout would be a tape contains #111111 and blank symbols afterward.


1 Answer 1


The language you describe is regular (because it's finite), so this can be really straight forward.

You could simple write a 1 and advance to the next state. Create 7 states, one state for each 1.

Consider input\output/direction the syntax for "if input is on the tape write output and move in direction"


  • $\begingroup$ I thought of this at solution at 1st glance actually, but I thought there is a more efficient way of achieving this. Thanks for your effort of course :) $\endgroup$
    – CSGuy
    Commented Dec 14, 2015 at 18:54
  • 1
    $\begingroup$ There are small machines that produce a large number of 1's, but to find them is not as easy as it seems. Have you heard of the Busy Beaver problem? $\endgroup$ Commented Dec 14, 2015 at 20:21
  • $\begingroup$ Well, you won't be more efficient, because you'd still have at least 7 steps. You could probably find a machine with fewer states, but that get's complicated. $\endgroup$
    – Sbls
    Commented Dec 15, 2015 at 16:18

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