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A CDCL-Style Calculus for Solving Non-linear Constraints

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Frontiers of Combining Systems (FroCoS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11715))

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Abstract

In this paper we propose a novel approach for checking satisfiability of non-linear constraints over the reals, called ksmt. The procedure is based on conflict resolution in CDCL-style calculus, using a composition of symbolical and numerical methods. To deal with the non-linear components in case of conflicts we use numerically constructed restricted linearisations. This approach covers a large number of computable non-linear real functions such as polynomials, rational or trigonometrical functions and beyond. A prototypical implementation has been evaluated on several non-linear SMT-LIB examples and the results have been compared with state-of-the-art SMT solvers.

The research leading to these results has received funding from the DFG grant WERA MU 1801/5-1 and the DFG/RFBR grant CAVER BE 1267/14-1 and 14-01-91334. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 731143.

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Notes

  1. 1.

    http://informatik.uni-trier.de/~brausse/ksmt.

  2. 2.

    http://irram.uni-trier.de.

  3. 3.

    ksmt-0.1.3, cvc4-1.6+gmp, z3-4.7.1+gmp, mathsat-5.5.2, yices-2.6+lpoly-1.7, dreal-v3.16.08.01, rasat-0.3.

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Acknowledgements

We thank the anonymous reviewers and Stefan Ratschan for their helpful comments.

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Correspondence to Franz Brauße .

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Brauße, F., Korovin, K., Korovina, M., Müller, N. (2019). A CDCL-Style Calculus for Solving Non-linear Constraints. In: Herzig, A., Popescu, A. (eds) Frontiers of Combining Systems. FroCoS 2019. Lecture Notes in Computer Science(), vol 11715. Springer, Cham. https://doi.org/10.1007/978-3-030-29007-8_8

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  • DOI: https://doi.org/10.1007/978-3-030-29007-8_8

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