Synthesizing Switching Logic Using Constraint Solving

  • Ankur Taly
  • Sumit Gulwani
  • Ashish Tiwari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5403)


A new approach based on constraint solving techniques was recently proposed for verification of hybrid systems. This approach works by searching for inductive invariants of a given form. In this paper, we extend that work to automatic synthesis of safe hybrid systems. Starting with a multi-modal dynamical system and a safety property, we present a sound technique for synthesizing a switching logic for changing modes so as to preserve the safety property. By construction, the synthesized hybrid system is well-formed and is guaranteed safe. Our approach is based on synthesizing a controlled invariant that is sufficient to prove safety. The generation of the controlled invariant is cast as a constraint solving problem. When the system, the safety property, and the controlled invariant are all expressed only using polynomials, the generated constraint is an ∃ ∀ formula in the theory of reals, which we solve using SMT solvers. The generated controlled invariant is then used to arrive at the maximally liberal switching logic.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ankur Taly
    • 1
  • Sumit Gulwani
    • 2
  • Ashish Tiwari
    • 3
  1. 1.Computer Science Dept.Stanford UniversityUSA
  2. 2.Microsoft ResearchRedmond
  3. 3.SRI InternationalMenlo Park

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