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Navigating the Universe of Z3 Theory Solvers

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Formal Methods: Foundations and Applications (SBMF 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12475))

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Abstract

Modular combination of theory solvers is an integral theme in engineering modern SMT solvers. The CDCL(T) architecture provides an overall setting for how theory solvers may cooperate around a SAT solver based on conflict driven clause learning. The Nelson-Oppen framework provides the interface contracts between theory solvers for disjoint signatures. This paper provides an update on theories integrated in Z3. We briefly review principles of theory integration in CDCL(T) and then examine the theory solvers available in Z3, with special emphasis on two recent solvers: a new solver for arithmetic and a pluggable user solver that allows callbacks to invoke propagations and detect conflicts.

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Notes

  1. 1.

    To keep the formula short we have applied a shortcut and removed the literal \(\lnot (x + y < 0)\) from the conflict clause. In practice, solvers automatically remove unit literals that are false from conflict clauses.

  2. 2.

    Thanks to Jasmin Blanchette for drawing attention to this distinction.

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Authors and Affiliations

  1. Microsoft Research, Washington, D.C., USA

    Nikolaj Bjørner & Lev Nachmanson

Authors
  1. Nikolaj Bjørner
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  2. Lev Nachmanson
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Correspondence to Nikolaj Bjørner .

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Editors and Affiliations

  1. Federal University of Pernambuco, Recife, Brazil

    Gustavo Carvalho

  2. Western Norway University of Applied Sciences, Bergen, Norway

    Volker Stolz

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Bjørner, N., Nachmanson, L. (2020). Navigating the Universe of Z3 Theory Solvers. In: Carvalho, G., Stolz, V. (eds) Formal Methods: Foundations and Applications. SBMF 2020. Lecture Notes in Computer Science(), vol 12475. Springer, Cham. https://doi.org/10.1007/978-3-030-63882-5_2

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  • DOI: https://doi.org/10.1007/978-3-030-63882-5_2

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