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

  • Daisuke IshiiEmail author
  • Kazunori Ueda
  • Hiroshi Hosobe
VSTTE 2009-2010


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.


Nonlinear hybrid systems Bounded model checking Satisfiability modulo theories Interval analysis 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.INRIA, LINA, Université de NantesNantesFrance
  2. 2.Department of Computer ScienceWaseda UniversityTokyoJapan
  3. 3.National Institute of InformaticsTokyoJapan

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