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An approximation algorithm for box abstraction of transition systems on real state spaces

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Abstract

Predicate abstraction is a powerful technique for extracting finite-state models from infinite-state systems such as computer software, and is applied to verification of safety properties. Predicate abstraction is also applied to verification of dynamical systems on real state spaces such as hybrid dynamical systems. In this paper, we propose a fast algorithm for computing entire abstract state spaces of transition systems on real state spaces. The method is based on the box abstraction of state spaces, and requires a relatively smaller number of reachability checks and Boolean operations. We also propose a fast method for computing the set of boxes that intersect a given convex polyhedron. This computation is a part of the proposed state-space generation algorithm. Effectiveness of the algorithm is evaluated by the computation time and by the difference of the approximated state space from the exact state space.

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Acknowledgements

The research is partly supported by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan, under Grant Nos. 21500009 and 20760278, and also by the Mitsutoyo Association for Science and Technology.

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  1. School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Ishikawa, 923-1292, Japan

    Kunihiko Hiraishi & Koich Kobayashi

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  1. Kunihiko Hiraishi
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  2. Koich Kobayashi
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Correspondence to Kunihiko Hiraishi.

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Hiraishi, K., Kobayashi, K. An approximation algorithm for box abstraction of transition systems on real state spaces. Form Methods Syst Des 42, 175–192 (2013). https://doi.org/10.1007/s10703-012-0175-z

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