We present an underapproximation for context-free languages by filtering out
runs of the underlying pushdown automaton depending on how the stack height
evolves over time. In particular, we assign to each run a number quantifying
the oscillating behavior of the stack along the run. We study languages
accepted by pushdown automata restricted to k-oscillating runs. We relate
oscillation on pushdown automata with a counterpart restriction on context-free
grammars. We also provide a way to filter all but the k-oscillating runs from a
given PDA by annotating stack symbols with information about the oscillation.
Finally, we study closure properties of the defined class of languages and the
complexity of the k-emptiness problem asking, given a pushdown automaton P and
k >= 0, whether P has a k-oscillating run. We show that, when k is not part of
the input, the k-emptiness problem is NLOGSPACE-complete.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.