On one-way Auxiliary pushdown automata

Abstract

A class of machines called one-way auxiliary pushdown automata, 1-APDA, is introduced. These machines differ from the well-known auxiliary pushdown automata by their input tape, which is one-way only. We restrict ourselves to f-tape-bounded 1-APDA with f(n) ≤ n and investigate some of their properties. In particular, it is shown:

• i) log log n is a lower bound for the tape complexity of 1-APDA to accept non-context-free languages, and this is a sharp bound.

• ii) If f(n) < n, i.e. if lim f(n) / n = O, then $\{ w_1 cw_2 c\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftarrow}$}}{w} _1 c\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftarrow}$}}{w} _2 /w_1 ,w_2 \varepsilon \{ o,1\} ^ * ,\left| {w_1 } \right| = \left| {w_2 } \right|\}$ is not accepted by any f-tape-bounded 1-APDA.

• iii) For every f with f(n) < n, nondeterministic f-tape-bounded 1-APDA are strictly more powerful than deterministic f-tape-bounded 1-APDA. This is in opposition to (two-way) auxiliary pushdown automata and to f-tape-bounded 1-APDA with f(n) ≥ c.n.