SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems

  • Andreas Eggers
  • Martin Fränzle
  • Christian Herde
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5311)


In order to facilitate automated reasoning about large Boolean combinations of non-linear arithmetic constraints involving ordinary differential equations (ODEs), we provide a seamless integration of safe numeric overapproximation of initial-value problems into a SAT-modulo-theory (SMT) approach to interval-based arithmetic constraint solving. Interval-based safe numeric approximation of ODEs is used as an interval contractor being able to narrow candidate sets in phase space in both temporal directions: post-images of ODEs (i.e., sets of states reachable from a set of initial values) are narrowed based on partial information about the initial values and, vice versa, pre-images are narrowed based on partial knowledge about post-sets.

In contrast to the related CLP(F) approach of Hickey and Wittenberg [12], we do (a) support coordinate transformations mitigating the wrapping effect encountered upon iterating interval-based overapproximations of reachable state sets and (b) embed the approach into an SMT framework, thus accelerating the solving process through the algorithmic enhancements of recent SAT solving technology.


Hybrid System Deduction Rule Equational Constraint Arithmetic Constraint Constraint Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andreas Eggers
    • 1
  • Martin Fränzle
    • 1
  • Christian Herde
    • 1
  1. 1.Dept. of CSCarl von Ossietzky Universität OldenburgGermany

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