A benders decomposition approach to deciding modular linear integer arithmetic

Bishoksan Kafle, Graeme Gange, Peter Schachte, Harald Søndergaard, Peter J. Stuckey

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

1 Citation (Scopus)


Verification tasks frequently require deciding systems of linear constraints over modular (machine) arithmetic. Existing approaches for reasoning over modular arithmetic use bit-vector solvers, or else approximate machine integers with mathematical integers and use arithmetic solvers. Neither is ideal; the first is sound but inefficient, and the second is efficient but unsound. We describe a linear encoding which correctly describes modular arithmetic semantics, yielding an optimistic but sound approach. Our method abstracts the problem with linear arithmetic, but progressively refines the abstraction when modular semantics is violated. This preserves soundness while exploiting the mostly integer nature of the constraint problem. We present a prototype implementation, which gives encouraging experimental results.

Original languageEnglish
Title of host publicationTheory and Applications of Satisfiability Testing – SAT 2017
Subtitle of host publication20th International Conference Melbourne, VIC, Australia, August 28 – September 1, 2017 Proceedings
EditorsSerge Gaspers, Toby Walsh
Place of PublicationCham Switzerland
Number of pages18
ISBN (Electronic)9783319662633
ISBN (Print)9783319662626
Publication statusPublished - 2017
Externally publishedYes
EventInternational Conference on Theory and Applications of Satisfiability Testing 2017 - Melbourne, Australia
Duration: 28 Aug 20171 Sept 2017
Conference number: 20th

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Conference on Theory and Applications of Satisfiability Testing 2017
Abbreviated titleSAT 2017
Internet address

Cite this