Nonerasing Stack Automata

The stack automaton has been recently introduced into the literature as a model for a compiler. The stack automaton has a two-way input tape, a finite control and a stack. The stack is similar to a push-down store, in that writing and erasing occur only at the top. However, the stack head may also move up or down the stack in a read only mode. Here, nonerasing stack automata only, are considered. These are stack automata that never erase a symbol from their stack. It is shown that the deterministic, nonerasing stack automaton is equivalent to a deterministic, off-line Turing machine whose storage tape never grows beyond n log"2n cells where n is the length of the input. Also, it is shown that the nondeterministic, nonerasing stack automaton is equivalent to a nondeterministic off-line Turing machine whose tape never grows beyond n^2 cells.