Pushdown automata with reversal-bounded counters

Abstract

The main result of this paper is that a pushdown automaton M augmented with R(n) reversal-bounded counters can be simulated by a Turing machine in time polynomial in n n 2 + R( n) if M is 2-way, and in time polynomial in n + R( n) if M is 1-way. It follows from this and previous results that for sufficiently large R(n), the addition of a pushdown store to R(n) reversal-bounded multicounter machines has little effect on the computing powers of the machines. The proof of the main result yields three interesting corollaries. First, relaxing the revversal bound from one counter in an R(n) reversal-bounded multicountter machine leads to very little increase in computing power. Second, 1-way pushdown automata augmented with 1-reversal counters accept in linear time and are therefore equivalent to 1-way simple multihead pushdown automata. Third, for every 1-way pushdown automaton, there is a constant c such that every accepting computation on an arbitrary nonempty input w contains a subsequence (of not necessarily consecutive operations) which is also an accepting computation on w and which has length at most c| w|.