Formal Verification of Bit-Vector Invertibility Conditions in Coq

Burak Ekici, Arjun Viswanathan, Yoni Zohar, Cesare Tinelli, Clark Barrett

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


We prove the correctness of invertibility conditions for the theory of fixed-width bit-vectors—used to solve quantified bit-vector formulas in the Satisfiability Modulo Theories (SMT) solver cvc5— in the Coq proof assistant. Previous work proved many of these in a completely automatic fashion for arbitrary bit-width; however, some were only proved for bit-widths up to 65, even though they are being used to solve formulas over larger bit-widths. In this paper we describe the process of proving a representative subset of these invertibility conditions in Coq. In particular, we describe the BVList library for bit-vectors in Coq, our extensions to it, and proofs of the invertibility conditions.

Original languageEnglish
Title of host publicationFrontiers of Combining Systems - 14th International Symposium, FroCoS 2023, Proceedings
EditorsUli Sattler, Martin Suda
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages19
ISBN (Print)9783031433689
StatePublished - 2023
Event14th International Symposium on Frontiers of Combining Systems, FroCoS 2023 - Prague, Czech Republic
Duration: 20 Sep 202322 Sep 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14279 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Symposium on Frontiers of Combining Systems, FroCoS 2023
Country/TerritoryCzech Republic

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).


Acknowledgements. This work was funded in part by NSF-BSF grant 2110397 (NSF) and 2020704 (BSF), and ISF grant number 619/21.

FundersFunder number
NSF-BSF2020704, 2110397
United States-Israel Binational Science Foundation
Israel Science Foundation619/21


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