Checking On-the-Fly Universality and Inclusion Problems of Visibly Pushdown Automata

Nguyen VAN TANG; Hitoshi OHSAKI

doi:10.1587/transfun.E94.A.2794

Checking On-the-Fly Universality and Inclusion Problems of Visibly Pushdown Automata

Nguyen VAN TANG, Hitoshi OHSAKI

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Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since it was introduced, VPA have been shown to be useful in various contexts, e.g., as specification formalism for verification and as an automaton model for processing XML streams. However, implementation of formal verification based on VPA framework is a challenge. In this paper, we propose on-the-fly algorithms to test universality and inclusion problems of this automata class. In particular, we first present a slight improvement on the upper bound for determinization of VPA. Next, in order to check universality of a nondeterministic VPA, we simultaneously determinize this VPA and apply the P-automata technique to compute a set of reachable configurations of the target determinized VPA. When a rejecting configuration is found, the checking process stops and reports that the original VPA is not universal. Otherwise, if all configurations are accepting, the original VPA is universal. Furthermore, to strengthen the algorithm, we define a partial ordering over transitions of P-automaton, and only minimal transitions are used to incrementally generate the P-automaton. The purpose of this process is to keep the determinization step implicitly for generating reachable configurations as minimum as possible. This improvement helps to reduce not only the size of the P-automaton but also the complexity of the determinization phase. We implement the proposed algorithms in a prototype tool, named VPAchecker. Finally, we conduct experiments on randomly generated VPA. The experimental results show that the proposed method outperforms the standard one by several orders of magnitude.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.12 pp.2794-2801

Publication Date: 2011/12/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E94.A.2794

Type of Manuscript: Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)

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Nguyen VAN TANG, Hitoshi OHSAKI, "Checking On-the-Fly Universality and Inclusion Problems of Visibly Pushdown Automata" in IEICE TRANSACTIONS on Fundamentals, vol. E94-A, no. 12, pp. 2794-2801, December 2011, doi: 10.1587/transfun.E94.A.2794.
Abstract: Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since it was introduced, VPA have been shown to be useful in various contexts, e.g., as specification formalism for verification and as an automaton model for processing XML streams. However, implementation of formal verification based on VPA framework is a challenge. In this paper, we propose on-the-fly algorithms to test universality and inclusion problems of this automata class. In particular, we first present a slight improvement on the upper bound for determinization of VPA. Next, in order to check universality of a nondeterministic VPA, we simultaneously determinize this VPA and apply the P-automata technique to compute a set of reachable configurations of the target determinized VPA. When a rejecting configuration is found, the checking process stops and reports that the original VPA is not universal. Otherwise, if all configurations are accepting, the original VPA is universal. Furthermore, to strengthen the algorithm, we define a partial ordering over transitions of P-automaton, and only minimal transitions are used to incrementally generate the P-automaton. The purpose of this process is to keep the determinization step implicitly for generating reachable configurations as minimum as possible. This improvement helps to reduce not only the size of the P-automaton but also the complexity of the determinization phase. We implement the proposed algorithms in a prototype tool, named VPAchecker. Finally, we conduct experiments on randomly generated VPA. The experimental results show that the proposed method outperforms the standard one by several orders of magnitude.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.2794/_p

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@ARTICLE{e94-a_12_2794,
author={Nguyen VAN TANG, Hitoshi OHSAKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Checking On-the-Fly Universality and Inclusion Problems of Visibly Pushdown Automata},
year={2011},
volume={E94-A},
number={12},
pages={2794-2801},
abstract={Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since it was introduced, VPA have been shown to be useful in various contexts, e.g., as specification formalism for verification and as an automaton model for processing XML streams. However, implementation of formal verification based on VPA framework is a challenge. In this paper, we propose on-the-fly algorithms to test universality and inclusion problems of this automata class. In particular, we first present a slight improvement on the upper bound for determinization of VPA. Next, in order to check universality of a nondeterministic VPA, we simultaneously determinize this VPA and apply the P-automata technique to compute a set of reachable configurations of the target determinized VPA. When a rejecting configuration is found, the checking process stops and reports that the original VPA is not universal. Otherwise, if all configurations are accepting, the original VPA is universal. Furthermore, to strengthen the algorithm, we define a partial ordering over transitions of P-automaton, and only minimal transitions are used to incrementally generate the P-automaton. The purpose of this process is to keep the determinization step implicitly for generating reachable configurations as minimum as possible. This improvement helps to reduce not only the size of the P-automaton but also the complexity of the determinization phase. We implement the proposed algorithms in a prototype tool, named VPAchecker. Finally, we conduct experiments on randomly generated VPA. The experimental results show that the proposed method outperforms the standard one by several orders of magnitude.},
keywords={},
doi={10.1587/transfun.E94.A.2794},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - Checking On-the-Fly Universality and Inclusion Problems of Visibly Pushdown Automata
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2794
EP - 2801
AU - Nguyen VAN TANG
AU - Hitoshi OHSAKI
PY - 2011
DO - 10.1587/transfun.E94.A.2794
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2011
AB - Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since it was introduced, VPA have been shown to be useful in various contexts, e.g., as specification formalism for verification and as an automaton model for processing XML streams. However, implementation of formal verification based on VPA framework is a challenge. In this paper, we propose on-the-fly algorithms to test universality and inclusion problems of this automata class. In particular, we first present a slight improvement on the upper bound for determinization of VPA. Next, in order to check universality of a nondeterministic VPA, we simultaneously determinize this VPA and apply the P-automata technique to compute a set of reachable configurations of the target determinized VPA. When a rejecting configuration is found, the checking process stops and reports that the original VPA is not universal. Otherwise, if all configurations are accepting, the original VPA is universal. Furthermore, to strengthen the algorithm, we define a partial ordering over transitions of P-automaton, and only minimal transitions are used to incrementally generate the P-automaton. The purpose of this process is to keep the determinization step implicitly for generating reachable configurations as minimum as possible. This improvement helps to reduce not only the size of the P-automaton but also the complexity of the determinization phase. We implement the proposed algorithms in a prototype tool, named VPAchecker. Finally, we conduct experiments on randomly generated VPA. The experimental results show that the proposed method outperforms the standard one by several orders of magnitude.
ER -