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Link to original content: https://doi.org/10.1007/s10009-011-0193-y
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An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems

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Abstract

This paper presents a bounded model checking tool called \({\texttt{Hydlogic}}\) for hybrid systems. It translates a reachability problem of a nonlinear hybrid system into a predicate logic formula involving arithmetic constraints and checks the satisfiability of the formula based on a satisfiability modulo theories method. We tightly integrate (i) an incremental SAT solver to enumerate the possible sets of constraints and (ii) an interval-based solver for hybrid constraint systems (HCSs) to solve the constraints described in the formulas. The HCS solver verifies the occurrence of a discrete change by using a set of boxes to enclose continuous states that may cause the discrete change. We utilize the existence property of a unique solution in the boxes computed by the HCS solver as (i) a proof of the reachability of a model and (ii) a guide in the over-approximation refinement procedure. Our \({\texttt{Hydlogic}}\) implementation successfully handled several examples including those with nonlinear constraints.

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Authors and Affiliations

  1. INRIA, LINA, Université de Nantes, 2, rue de la Houssinière, 44322, Nantes, France

    Daisuke Ishii

  2. Department of Computer Science, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Kazunori Ueda

  3. National Institute of Informatics, 2-1-2, Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Hiroshi Hosobe

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  1. Daisuke Ishii
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  2. Kazunori Ueda
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  3. Hiroshi Hosobe
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Correspondence to Daisuke Ishii.

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Ishii, D., Ueda, K. & Hosobe, H. An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems. Int J Softw Tools Technol Transfer 13, 449–461 (2011). https://doi.org/10.1007/s10009-011-0193-y

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