Big gaps between RAM and Turing machine complexity If we only consider problems in P, are there any big gaps between the fastest known word-RAM algorithm and the fastest known Turing machine algorithm for particular problems? I am particularly interested if there are wide gaps for natural problems of general interest.
It is known that any problem that you can compute on a RAM machine in time $T(n)$, you can do it in a Turing Machine in time at most $T(n)^2$. You need to notice that the total size of the memory used can not be more than $T(n)$, since that would mean that you did more write operations than $T(n)$, so each time you fetch something from RAM memory, the Turing machine would take in the worst case $T(n)$ time to find the desired element sequentially from the tape. Besides memory access, the rest of operations should take around the same time. And thus you get the bound.