2-Visibly Pushdown Automata
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- Carotenuto D., Murano A., Peron A. (2007) 2-Visibly Pushdown Automata. In: Harju T., Karhumäki J., Lepistö A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg
Visibly Pushdown Automata (VPA) are a special case of pushdown machines where the stack operations are driven by the input. In this paper, we consider VPA with two stacks, namely 2-VPA. These automata introduce a useful model to effectively describe concurrent pushdown systems using a simple communication mechanism between stacks. We show that 2-VPA are strictly more expressive than VPA. Indeed, 2-VPA accept some context-sensitive languages that are not context-free and some context-free languages that are not accepted by any VPA. Nevertheless, the class of languages accepted by 2-VPA is closed under all boolean operations and determinizable in ExpTime, but does not preserve decidability of emptiness problem. By adding an ordering constraint on stacks (2-OVPA), decidability of emptiness can be recovered (preserving desirable closure properties) and solved in PTime. Using these properties along with the automata-theoretic approach, we prove that the model checking problem over 2-OVPA models against 2-OVPA specifications is ExpTime-complete.
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