2016/09/14 by Pierre Ganty, Damir Valput
Computer Science · #cs.FL #cs.CC
paper · pdf · doi:10.4204/eptcs.226.13
published as EPTCS 226, 2016, pp. 178-197 · In Proceedings GandALF 2016, arXiv:1609.03648
arxiv created 2016/09/14 · arxiv updated 2016/09/15
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.