On the equivalence of two-way pushdown automata and counter machines over bounded languages

Abstract

It is known that two-way pushdown automata ate more powerful than two-way counter machines. The result is also true for the case when the pushdown store and counter are reversal-bounded. In contrast, we show that two-way reversal-bounded pushdown automata over bounded languages (i.e., subsets of w 1 * ... w k * for some nonnull words w1 ..., wk) are equivalent to two-way reversal-bounded counter machines. We also show that, unlike the unbounded input case, two-way reversal-bounded pushdown automata over bounded languages have decidable emptiness, equivalence and containment problems.