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SAT-Based Invariant Inference and Its Relation to Concept Learning

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Reachability Problems (RP 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13608))

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Abstract

This paper surveys results that establish formal connections and distinctions between SAT-based invariant inference and exact concept learning with queries, showing that learning techniques and algorithms can clarify foundational questions, illuminate existing algorithms, and suggest new directions for efficient invariant inference.

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Notes

  1. 1.

    A notable exception is ternary simulation [8], which is not a SAT-based operation. However, the query model can be extended to support it while maintaining our results.

  2. 2.

    In [10], the invariants are antimonotone rather than monotone; the algorithm establishing the upper bound is efficient also for monotone invariants, and the proof of the lower bound can also be adapted to monotone invariants.

  3. 3.

    To be precise, in PDR, counterexamples are states that reach a bad state, whereas PDR-1 uses counterexamples to induction, but these coincide in maximal systems; additionally, PDR may use an additional frame to discover the counterexamples and one more to detect convergence.

  4. 4.

    In general, a concept is a set of elements; here we focus on logical concepts.

  5. 5.

    The proof of this also implies that an invariant that is both forwards \(k_1\)-fenced and backwards \(k_2\)-fenced is unique, seeing that the implementation of the membership query for both is the same.

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Acknowledgement

The research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. [759102-SVIS]). This research was partially supported by the United States-Israel Binational Science Foundation (BSF) grant No. 2016260, and the Israeli Science Foundation (ISF) grant No. 1810/18.

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  1. Tel Aviv University, Tel Aviv, Israel

    Yotam M. Y. Feldman & Sharon Shoham

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  1. Yotam M. Y. Feldman
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Correspondence to Sharon Shoham .

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  1. Department of Computer Science, TU Kaiserslautern, Kaiserslautern, Germany

    Anthony W. Lin

  2. Max Planck Institute for Software Systems, Kaiserslautern, Germany

    Georg Zetzsche

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

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Feldman, Y.M.Y., Shoham, S. (2022). SAT-Based Invariant Inference and Its Relation to Concept Learning. In: Lin, A.W., Zetzsche, G., Potapov, I. (eds) Reachability Problems. RP 2022. Lecture Notes in Computer Science, vol 13608. Springer, Cham. https://doi.org/10.1007/978-3-031-19135-0_1

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