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 proceedingConference contributionpeer-review

4 Scopus citations


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 languageEnglish
Title of host publicationAutomated Deduction – CADE 2019- 27th International Conference on Automated Deduction, Proceedings
EditorsPascal Fontaine
Number of pages19
ISBN (Print)9783030294359
StatePublished - 2019
Externally publishedYes
Event27th International Conference on Automated Deduction, CADE 2019 - Natal, Brazil
Duration: 27 Aug 201930 Aug 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11716 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th International Conference on Automated Deduction, CADE 2019

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© Springer Nature Switzerland AG 2019.


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