Consider the following:
A weak TM is a TM with finite tape in size $k$ which can only read its input values. note: the tape size does not include the input length.
I need to determine whether if the weak model is equivalent to a regular TM, or to explain why not and to show the equivalence to any other computational model.
I'm quiet confident that the weak TM is equivalent to a DFA with $\gamma^k\cdot q\cdot (n+k)$ states where $|\Gamma| = \gamma$, $|Q| = q$ and $|w| = n$.
My intuition is that there are at most $\gamma^k$ strings that the machine can write, there are $q$ states and the head can be stationed at one of the $n+k$ slots on the tape.
I'm having a hard time to prove it though, Anyone can shed some light?