1
$\begingroup$

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)?

$\endgroup$
  • $\begingroup$ after the input word ends I take this to apply to both "ends". $\endgroup$ – greybeard May 23 at 10:34
1
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ got it, thanks a lot! $\endgroup$ – Stephan May 22 at 15:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.