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Incremental Search for Conflict and Unit Instances of Quantified Formulas with E-Matching

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12597))

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Abstract

We present a new method to find conflicting instances of quantified formulas in the context of SMT solving. Our method splits the search for such instances in two parts. In the first part, E-matching is used to find candidate instances of the quantified formulas. In principle, any existing incremental E-matching technique can be used. The incrementality avoids duplicating work for each small change of the E-graph. Together with the candidate instance, E-matching also provides an existing node in the E-graph corresponding to each term in this instance. In the second part, these nodes are used to evaluate the candidate instance, i.e., without creating new terms. The evaluation can be done in constant time per instance. Our method detects conflicting instances and unit-propagating instances (clauses that propagate new literals). This makes our method suitable for a tight integration with the DPLL(\(\mathcal {T}\)) framework, very much in the style of an additional theory solver.

Partially supported by the German Research Council (DFG) under HO 5606/1-2.

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Notes

  1. 1.

    From now on \(\sim \) denotes the congruence closure of the equality edges in the E-graph and not the transitive closure as in the previous section. Note that this is also defined for \(p\sigma \), if it does not exist in the E-graph.

  2. 2.

    https://ultimate.informatik.uni-freiburg.de/smtinterpol/

  3. 3.

    https://smt-comp.github.io/2020/

  4. 4.

    https://www.starexec.org

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Authors and Affiliations

  1. University of Freiburg, Freiburg im Breisgau, Germany

    Jochen Hoenicke & Tanja Schindler

Authors
  1. Jochen Hoenicke
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  2. Tanja Schindler
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Correspondence to Jochen Hoenicke or Tanja Schindler .

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Editors and Affiliations

  1. University of Copenhagen, Copenhagen, Denmark

    Fritz Henglein

  2. Tel Aviv University, Tel Aviv, Israel

    Sharon Shoham

  3. Technion, Haifa, Israel

    Yakir Vizel

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Hoenicke, J., Schindler, T. (2021). Incremental Search for Conflict and Unit Instances of Quantified Formulas with E-Matching. In: Henglein, F., Shoham, S., Vizel, Y. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2021. Lecture Notes in Computer Science(), vol 12597. Springer, Cham. https://doi.org/10.1007/978-3-030-67067-2_24

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