# Turing machine with a finite tape after the input word ends

How can I prove that for a natural number K, a language that accepted by a Turing machine with K cells after the input word ends, belongs to R (which R is the set of languages that there is Turing machine that accept them while for each input the run is finite)?

• after the input word ends I take this to apply to both "ends". May 23 '20 at 10:34

## 1 Answer

Given the length of the input $$n$$, you can come up with a bound $$N(n)$$ on the number of configurations that the Turing machine can have. If the machine hasn't stopped on an input within $$N(n)$$ time steps, then it will never stop (why?), and you can use this to complete the proof. Details left to you.

• got it, thanks a lot! May 22 '20 at 15:36