An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems

Daisuke Ishii, Kazunori Ueda, Hiroshi Hosobe

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    21 Citations (Scopus)


    This paper presents a bounded model checking tool called 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 implementation successfully handled several examples including those with nonlinear constraints.

    Original languageEnglish
    Pages (from-to)449-461
    Number of pages13
    JournalInternational Journal on Software Tools for Technology Transfer
    Issue number5
    Publication statusPublished - 2011 Oct



    • Bounded model checking
    • Interval analysis
    • Nonlinear hybrid systems
    • Satisfiability modulo theories

    ASJC Scopus subject areas

    • Software
    • Information Systems

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