# Space penalties for the simulation of a non-deterministic Turing machine by a single-tape deterministic Turing machine

If I have some non-deterministic Turing machine $NDTM$ running some process $Q$ and I wish to simulate the same process $Q$ with a deterministic single-tape Turing machine $DTM$, there will of course be an exponential slowdown. However, what penalty can one expect in terms of space resources? Unless one has access to an $RNG$, presumably one has to keep track of which configurations one has already tried? Can we simulate the $NDTM$ with the $DTM$ using only polynomially more space?

Savitch's theorem shows that $\mathsf{NSPACE}(f(n)) \subseteq \mathsf{SPACE}(f(n)^2)$.