Improving SAT Modulo ODE for Hybrid Systems Analysis by Combining Different Enclosure Methods

  • Andreas Eggers
  • Nacim Ramdani
  • Nedialko Nedialkov
  • Martin Fränzle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7041)


Aiming at automatic verification and analysis techniques for hybrid systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT with VNODE-LP, as a state-of-the-art enclosure method for ODEs, and with bracketing systems which exploit monotonicity properties to find enclosures for problems that VNODE-LP alone cannot enclose tightly. We apply our method to the analysis of a non-linear hybrid system by solving predicative encodings of an inductive stability argument and evaluate the impact of different methods and their combination.


Hybrid System Proof Obligation Arithmetic Constraint Current Partial Assignment Delta Time 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andreas Eggers
    • 1
  • Nacim Ramdani
    • 2
  • Nedialko Nedialkov
    • 3
  • Martin Fränzle
    • 1
  1. 1.Carl von Ossietzky UniversitätOldenburgGermany
  2. 2.Université d’Orléans, PRISMEBourgesFrance
  3. 3.McMaster UniversityHamiltonCanada

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