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Structure-Guided Solution of Constrained Horn Clauses

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Automated Technology for Verification and Analysis (ATVA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14216))

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Abstract

We present \({\textsf {StHorn}} \), a novel technique for solving the satisfiability problem of CHCs, which works lazily and incrementally and is guided by the structure of the set of CHCs. Our technique is driven by the idea that a set of CHCs can be solved in parts, making it an easier problem for the CHC-solver. Furthermore, solving a set of CHCs can benefit from an interpretation revealed by the solver for its subsets. Our technique is lazy in that it gradually extends the set of checked CHCs, as needed. It is incremental in the way it constructs a solution by using satisfying interpretations obtained for previously checked subsets. In order to capture the structure of the problem, we define an induced CHC hypergraph that precisely corresponds to the set of CHCs. The paths in this graph are explored and used to select the clauses to be solved.

We implemented StHorn on top of two CHC-solvers, Spacer and Eldarica. Our evaluation shows that StHorn complements both tools and can solve instances that cannot be solved by the other tools. We conclude that StHorn can improve upon the state-of-the-art in CHC solving.

This research is partially funded by the Israel Science Foundation (ISF), grant no. 2875/21.

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Notes

  1. 1.

    This weight function is called the traversal cost in [1]. For this weight function, computing the shortest nontrivial hyperpath (see Sect. 4) is polynomial.

  2. 2.

    The underlying CHC-solver may also return UNKNOWN. This case can be handled similarly to the case where SAT is returned and is omitted for simplicity of presentation.

  3. 3.

    Strengthening can be achieved as follows: if \(\mathcal {I}\models _{r}\varPi \) and \(\mathcal {{I'}}\models \varPi \) then the interpretation that maps every \(p\in \mathcal {P}^{\varPi }\) to \(\mathcal {I}(p)\wedge \mathcal {{I'}}(p)\) satisfies \(\varPi \).

  4. 4.

    We assume, w.l.o.g., that the head of a query is \(\bot \).

  5. 5.

    In fact, the induced CHC hypergraph may include parallel hyperedges originating from two CHCs that differ only in their constraints. While we support such a case, we omit it here for simplicity of presentation.

  6. 6.

    We were not able to find such a parameter for Eldarica.

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Authors and Affiliations

  1. Technion - Israel Institute of Technology, Haifa, Israel

    Omer Rappoport, Orna Grumberg & Yakir Vizel

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  1. Omer Rappoport
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  1. Université Sorbonne Paris Nord, Villetaneuse, France

    Étienne André

  2. Singapore Management University, Singapore, Singapore

    Jun Sun

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Rappoport, O., Grumberg, O., Vizel, Y. (2023). Structure-Guided Solution of Constrained Horn Clauses. In: André, É., Sun, J. (eds) Automated Technology for Verification and Analysis. ATVA 2023. Lecture Notes in Computer Science, vol 14216. Springer, Cham. https://doi.org/10.1007/978-3-031-45332-8_6

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