So let's say I've implemented an algorithm running in $O(n^2)$ on my 3-tape TM. What kind of time complexity would I expect for a single-tape TM?

I just don't know where to get started...


1 Answer 1


Multi-tape Turing Machine running in $O(f(n))$ can be simulated by a single-tape Turing machine running in $O(f^2(n))$.

Try writing a single-tape Turing machine that stores symbols from your $3$ tapes on its one tape, separated by some unique symbol not in $\Sigma$.

hint: For every step of your $k$-tape machine, a one-tape machine must first do at most $k\cdot n$ steps to find the position.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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