Towards bit-width-independent proofs in SMT solvers

Aina Niemetz; Mathias Preiner; Andrew Reynolds; Yoni Zohar; Clark Barrett; Cesare Tinelli

doi:10.1007/978-3-030-29436-6_22

Towards bit-width-independent proofs in SMT solvers

Aina Niemetz, Mathias Preiner, Andrew Reynolds, Yoni Zohar, Clark Barrett, Cesare Tinelli

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

Many SMT solvers implement efficient SAT-based procedures for solving fixed-size bit-vector formulas. These approaches, however, cannot be used directly to reason about bit-vectors of symbolic bit-width. To address this shortcoming, we propose a translation from bit-vector formulas with parametric bit-width to formulas in a logic supported by SMT solvers that includes non-linear integer arithmetic, uninterpreted functions, and universal quantification. While this logic is undecidable, this approach can still solve many formulas by capitalizing on advances in SMT solving for non-linear arithmetic and universally quantified formulas. We provide several case studies in which we have applied this approach with promising results, including the bit-width independent verification of invertibility conditions, compiler optimizations, and bit-vector rewrites.

Original language	English
Title of host publication	Automated Deduction – CADE 2019- 27th International Conference on Automated Deduction, Proceedings
Editors	Pascal Fontaine
Publisher	Springer
Pages	366-384
Number of pages	19
ISBN (Print)	9783030294359
DOIs	https://doi.org/10.1007/978-3-030-29436-6_22
State	Published - 2019
Externally published	Yes
Event	27th International Conference on Automated Deduction, CADE 2019 - Natal, Brazil Duration: 27 Aug 2019 → 30 Aug 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11716 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Conference on Automated Deduction, CADE 2019
Country/Territory	Brazil
City	Natal
Period	27/08/19 → 30/08/19

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Funding

This work was supported in part by DARPA (awards N66001-18-C-4012 and FA8650-18-2-7861), ONR (award N68335-17-C-0558), NSF (award 1656926), and the Stanford Center for Blockchain Research.

Funders	Funder number
Stanford Center for Blockchain Research
National Science Foundation	1656926
Office of Naval Research	N68335-17-C-0558
Defense Advanced Research Projects Agency	FA8650-18-2-7861, N66001-18-C-4012

Access to Document

10.1007/978-3-030-29436-6_22

Cite this

Niemetz, A., Preiner, M., Reynolds, A., Zohar, Y., Barrett, C., & Tinelli, C. (2019). Towards bit-width-independent proofs in SMT solvers. In P. Fontaine (Ed.), Automated Deduction – CADE 2019- 27th International Conference on Automated Deduction, Proceedings (pp. 366-384). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11716 LNAI). Springer. https://doi.org/10.1007/978-3-030-29436-6_22

Niemetz, Aina ; Preiner, Mathias ; Reynolds, Andrew et al. / Towards bit-width-independent proofs in SMT solvers. Automated Deduction – CADE 2019- 27th International Conference on Automated Deduction, Proceedings. editor / Pascal Fontaine. Springer, 2019. pp. 366-384 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Many SMT solvers implement efficient SAT-based procedures for solving fixed-size bit-vector formulas. These approaches, however, cannot be used directly to reason about bit-vectors of symbolic bit-width. To address this shortcoming, we propose a translation from bit-vector formulas with parametric bit-width to formulas in a logic supported by SMT solvers that includes non-linear integer arithmetic, uninterpreted functions, and universal quantification. While this logic is undecidable, this approach can still solve many formulas by capitalizing on advances in SMT solving for non-linear arithmetic and universally quantified formulas. We provide several case studies in which we have applied this approach with promising results, including the bit-width independent verification of invertibility conditions, compiler optimizations, and bit-vector rewrites.",

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Niemetz, A, Preiner, M, Reynolds, A, Zohar, Y, Barrett, C & Tinelli, C 2019, Towards bit-width-independent proofs in SMT solvers. in P Fontaine (ed.), Automated Deduction – CADE 2019- 27th International Conference on Automated Deduction, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11716 LNAI, Springer, pp. 366-384, 27th International Conference on Automated Deduction, CADE 2019, Natal, Brazil, 27/08/19. https://doi.org/10.1007/978-3-030-29436-6_22

Towards bit-width-independent proofs in SMT solvers. / Niemetz, Aina; Preiner, Mathias; Reynolds, Andrew et al.
Automated Deduction – CADE 2019- 27th International Conference on Automated Deduction, Proceedings. ed. / Pascal Fontaine. Springer, 2019. p. 366-384 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11716 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Niemetz A, Preiner M, Reynolds A, Zohar Y, Barrett C, Tinelli C. Towards bit-width-independent proofs in SMT solvers. In Fontaine P, editor, Automated Deduction – CADE 2019- 27th International Conference on Automated Deduction, Proceedings. Springer. 2019. p. 366-384. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-29436-6_22

Towards bit-width-independent proofs in SMT solvers

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