Reversal-bounded and visit-bounded realtime computations

Abstract

First it is dealt with the class RBQ (also sometimes called BNP) of all languages acceptable in linear time by reversal-bounded nondeterministic multitape Turing machines.

It has been shown (see /2/) that the RBQ languages can already be accepted by nondeterministic realtime machines having only three pushdown stores and working with at most one reversal per pushdown store. We show that these three pushdown stores can be replaced by two checking stacks each making at most two reversals. In this result "two" cannot be replaced by "one" because of a recent result by HULL (see /7/).

The class RBQ is known to be closed under intersection and the AFL operations except for Kleene star. It is conjectured that RBQ is not closed under Kleene star (see /3/). We show that the least intersection closed AFL containing RBQ (or, equivalently, the least intersection closed semi-AFL containing the set PAL^*) coincides with the class VBQ of all languages acceptable in linear time by visit-bounded nondeterministic multitape Turing machines. Furthermore, the VBQ languages can already be accepted by nondeterministic realtime machines having only three pushdown stores and working with at most 3 visits (or, equivalently, having only two checking stacks and working with at most 4 visits). These results cannot be improved unless RBQ=VBQ.