There are languages that a Turing machine can handle that an LBA can't, but are there any useful, practical problems that LBAs can't solve but TMs can?
An LBA is just a Turing machine with a finite tape, and actual computers have finite storage, so it would seem to me that there's nothing of practical importance that an LBA can't do. Except for the fact that a Linear Bounded Automaton has not just a finite tape, but a tape with a size that's a linear function of the size of the input. Does the linearity of the finiteness restrict the LBA in some way?
Are there problems that a LBA can't cope with, but an Exponentially Bounded Automaton could (if such things exist)?