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Interpolation with guided refinement: revisiting incrementality in SAT-based unbounded model checking

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Abstract

This paper addresses model checking based on SAT solvers and Craig interpolants. We tackle major scalability problems of state-of-the-art interpolation-based approaches, and we achieve two main results: (1) A novel model checking algorithm; (2) A new and flexible way to handle an incremental representation of (over-approximated) forward reachable states. The new model checking algorithm IGR, Interpolation with Guided Refinement, partially takes inspiration from IC3 and interpolation sequences. It bases its robustness and scalability on incremental refinement of state sets, and guided unwinding/simplification of transition relation unrollings. State sets, the central data structure of our algorithm, are incrementally refined, and they represent a valuable information to be shared among related problems, either in concurrent or sequential (multiple-engine or multiple-property) execution schemes. We provide experimental data, showing that IGR extends the capability of a state-of-the-art model checker, with a specific focus on hard-to-prove properties.

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Notes

  1. We use the notation \({\mathbf {F}}_{\mathbf {i}}\) instead of \(F_i\) to refer to a frame of \({\mathbf {F}}_{\mathbf {k}}\) that does not exists yet and that is being initialized for the first time.

  2. Following [8], we heuristically increment cone bounds by more than 1, based on the depth of the previous ApproxFwdTrav run.

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Authors and Affiliations

  1. Dipartimento di Automatica ed Informatica, Politecnico di Torino, Turin, Italy

    G. Cabodi, P. E. Camurati, M. Palena & P. Pasini

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  1. G. Cabodi
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  2. P. E. Camurati
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  3. M. Palena
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  4. P. Pasini
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Correspondence to M. Palena.

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A preliminary version [1] of this paper was presented at FMCAD2014 http://www.cs.utexas.edu/users/hunt/FMCAD/FMCAD14/index.shtml/.

This work was supported in part by SRC contract 2012-TJ-2328.

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Cabodi, G., Camurati, P.E., Palena, M. et al. Interpolation with guided refinement: revisiting incrementality in SAT-based unbounded model checking. Form Methods Syst Des 60, 117–146 (2022). https://doi.org/10.1007/s10703-022-00406-7

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