Automata-Theoretic techniques for modal logics of programs
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Distributed Systems: Principles and Paradigms
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STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computation: finite and infinite machines
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LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Membership Testing: Removing Extra Stacks from Multi-stack Pushdown Automata
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
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SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
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LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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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.