Abstract
It is shown that one-way deterministic reversal-bounded multicounter languages are closed under right quotient with languages from many language families; even those defined by nondeterministic machines such as the context-free languages. Also, it is shown that when starting with one-way deterministic machines with one counter that makes only one reversal, taking the left quotient with languages from many different language families — again including those defined by nondeterministic machines such as the context-free languages — yields only one-way deterministic reversal-bounded multicounter languages. These results are surprising given the nondeterministic nature of the deletion. However, if there are two more reversals on the counter, or a second 1-reversal-bounded counter, taking the left quotient (or even just the suffix operation) yields languages that can neither be accepted by deterministic reversal-bounded multi-counter machines, nor by 2-way deterministic machines with one reversal-bounded counter.
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