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Wombit: A Portfolio Bit-Vector Solver Using Word-Level Propagation

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Abstract

We develop an idea originally proposed by Michel and Van Hentenryck of how to perform bit-vector constraint propagation on the word level. Most operations are propagated in constant time, assuming the bit-vector fits in a machine word. In contrast, bit-vector SMT solvers usually solve bit-vector problems by (ultimately) bit-blasting, that is, mapping the resulting operations to conjunctive normal form clauses, and using SAT technology to solve them. Bit-blasting generates intermediate variables which can be an advantage, as these can be searched on and learnt about. As each approach has advantages, it makes sense to try to combine them. In this paper, we describe an approach to bit-vector solving using word-level propagation with learning. We have designed alternative word-level propagators to Michel and Van Hentenryck’s, and evaluated different variants of the approach. We have also experimented with different approaches to learning and back-jumping in the solver. Based on the insights gained, we have built a portfolio solver, Wombit, which essentially extends the STP bit-vector solver. Using machine learning techniques, the solver makes a judicious up-front decision about whether to use word-level propagation or fall back on bit-blasting.

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Notes

  1. In some formalisations of propagation, the idempotence requirement is dropped, primarily for technical reasons—to ensure that the set of propagators is closed under function composition.

  2. The propagation rules for \(z=\mathbf {ite^{BV}}(bv, x, y)\) differ substantially from those in [50] which are: \( low^y = l^y~|~(l^z~ \& ~ (l^{bv}~|~(\sim u^x)))\) and \( up^y = u^y~ \& ~ \sim (\sim u^z ~ \& ~ (l^{bv} ~|~ l^x))\) (using our notation). These rules are not quite correct. For example, for bit-width 1, let \(z=1\), \(bv=0\), and let x and y be unknown, then y should be fixed to 1. But under the rule above, \(low^y=0\), which is an error.

  3. https://www.starexec.org/starexec/secure/explore/spaces.jsp?id=2641

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Acknowledgements

We wish to thank the reviewers of this paper for very detailed and helpful comments and suggestions. We acknowledge support from the Australian Research Council through ARC Discovery Grant DP140102194.

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Authors and Affiliations

  1. Department of Electrical and Computing Engineering, The University of Texas at Austin, Austin, TX, 78712, USA

    Wenxi Wang

  2. School of Computing and Information Systems, The University of Melbourne, Parkville, VIC, 3010, Australia

    Harald Søndergaard

  3. Faculty of IT, Monash University, 900 Dandenong Road, Caulfield East, VIC, 3145, Australia

    Peter J. Stuckey

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Wang, W., Søndergaard, H. & Stuckey, P.J. Wombit: A Portfolio Bit-Vector Solver Using Word-Level Propagation. J Autom Reasoning 63, 723–762 (2019). https://doi.org/10.1007/s10817-018-9493-1

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