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Heterogeneous Heuristic Optimisation and Scheduling for First-Order Theorem Proving

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Intelligent Computer Mathematics (CICM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12833))

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Abstract

Good heuristics are essential for successful proof search in first-order automated theorem proving. As a result, state-of-the-art theorem provers offer a range of options for tuning the proof search process to specific problems. However, the vast configuration space makes it exceedingly challenging to construct effective heuristics. In this paper we present a new approach called HOS-ML, for automatically discovering new heuristics and mapping problems into optimised local schedules comprising of these heuristics. Our approach is based on interleaving Bayesian hyper-parameter optimisation for discovering promising heuristics and dynamic clustering to make optimisation efficient on heterogeneous problems. HOS-ML also use constraint programming to devise locally optimal schedules and machine learning for mapping unseen problems into such schedules. We evaluated HOS-ML on the theorem prover iProver and demonstrated that it can discover new heuristics that considerably improve performance and can solve problems that have not been solved previously by any other system.

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Notes

  1. 1.

    Heuristic discovery is available at: https://gitlab.com/korovin/iprover-smac.

  2. 2.

    CP-SAT is available at: https://github.com/google/or-tools.

  3. 3.

    Schedule computation is available at: https://gitlab.com/edvardholden/scpeduler.

  4. 4.

    kneed is available at: https://github.com/arvkevi/kneed.

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Authors and Affiliations

  1. The University of Manchester, Manchester, UK

    Edvard K. Holden & Konstantin Korovin

Authors
  1. Edvard K. Holden
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  2. Konstantin Korovin
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Correspondence to Edvard K. Holden .

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Editors and Affiliations

  1. Heriot-Watt University, Edinburgh, UK

    Fairouz Kamareddine

  2. University of Bologna, Bologna, Italy

    Claudio Sacerdoti Coen

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Holden, E.K., Korovin, K. (2021). Heterogeneous Heuristic Optimisation and Scheduling for First-Order Theorem Proving. In: Kamareddine, F., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2021. Lecture Notes in Computer Science(), vol 12833. Springer, Cham. https://doi.org/10.1007/978-3-030-81097-9_8

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  • DOI: https://doi.org/10.1007/978-3-030-81097-9_8

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