Bounded-oscillation Pushdown Automata

Pierre Ganty
(IMDEA Software Institute, Madrid, Spain)
Damir Valput
(IMDEA Software Institute, Madrid, Spain)

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.

In Domenico Cantone and Giorgio Delzanno: Proceedings of the Seventh International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2016), Catania, Italy, 14-16 September 2016, Electronic Proceedings in Theoretical Computer Science 226, pp. 178–197.
Published: 13th September 2016.

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