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Learning Linear Temporal Properties from Noisy Data: A MaxSAT-Based Approach

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 12971)

Abstract

We address the problem of inferring descriptions of system behavior using Linear Temporal Logic (LTL) from a finite set of positive and negative examples. Most of the existing approaches for solving such a task rely on predefined templates for guiding the structure of the inferred formula. The approaches that can infer arbitrary LTL formulas, on the other hand, are not robust to noise in the data. To alleviate such limitations, we devise two algorithms for inferring concise LTL formulas even in the presence of noise. Our first algorithm infers minimal LTL formulas by reducing the inference problem to a problem in maximum satisfiability and then using off-the-shelf MaxSAT solvers to find a solution. To the best of our knowledge, we are the first to incorporate the usage of MaxSAT solvers for inferring formulas in LTL. Our second learning algorithm relies on the first algorithm to derive a decision tree over LTL formulas based on a decision tree learning algorithm. We have implemented both our algorithms and verified that our algorithms are efficient in extracting concise LTL descriptions even in the presence of noise.

Keywords

  • Linear temporal logic
  • Specification mining
  • Explainable AI

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Notes

  1. 1.

    LTL, when interpreted over finite traces, is sometimes referred to as LTLf.

  2. 2.

    We adapted SAT-DT to learn decision trees with a similar stopping criteria as ours.

  3. 3.

    https://github.com/cryhot/samples2LTL.

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Acknowledgements

This work has been supported by the Defense Advanced Research Projects Agency (DARPA) under Contract no. HR001120C0032, ARL W911NF2020132, ARL ACC-APG-RTP W911NF, NSF 1646522 and DFG Grant no. 434592664.

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Correspondence to Rajarshi Roy .

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Gaglione, JR., Neider, D., Roy, R., Topcu, U., Xu, Z. (2021). Learning Linear Temporal Properties from Noisy Data: A MaxSAT-Based Approach. In: Hou, Z., Ganesh, V. (eds) Automated Technology for Verification and Analysis. ATVA 2021. Lecture Notes in Computer Science(), vol 12971. Springer, Cham. https://doi.org/10.1007/978-3-030-88885-5_6

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  • DOI: https://doi.org/10.1007/978-3-030-88885-5_6

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