Towards Conflict-Driven Learning for Virtual Substitution

  • Konstantin Korovin
  • Marek Kos̆ta
  • Thomas Sturm
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8660)


We consider satisfiability modulo theory-solving for linear real arithmetic. Inspired by related work for the Fourier–Motzkin method, we combine virtual substitution with learning strategies. For the first time, we present virtual substitution—including our learning strategies—as a formal calculus. We prove soundness and completeness for that calculus. Some standard linear programming benchmarks computed with an experimental implementation of our calculus show that the integration of learning techniques into virtual substitution gives rise to considerable speedups. Our implementation is open-source and freely available.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Konstantin Korovin
    • 1
  • Marek Kos̆ta
    • 2
  • Thomas Sturm
    • 2
  1. 1.The University of ManchesterUK
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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