Solving Using Approximations

Maxwell Levatich, Nikolaj Bjørner*, Ruzica Piskac, Sharon Shoham

*Corresponding author for this work

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

3 Scopus citations

Abstract

Linear arithmetic with stars,, is an extension of Presburger arithmetic that allows forming indefinite summations over values that satisfy a formula. It has found uses in decision procedures for multi-sets and for vector addition systems. formulas can be translated back into Presburger arithmetic, but with non-trivial space overhead. In this paper we develop a decision procedure for that checks satisfiability of formulas. By refining on-demand under and over-approximations of formulas, it can avoid the space overhead that is integral to previous approaches. We have implemented our procedure in a prototype and report on encouraging results that suggest that formulas can be checked for satisfiability without computing a prohibitively large equivalent Presburger formula.

Original languageEnglish
Title of host publicationVerification, Model Checking, and Abstract Interpretation - 21st International Conference, VMCAI 2020, Proceedings
EditorsDirk Beyer, Damien Zufferey
PublisherSpringer
Pages360-378
Number of pages19
ISBN (Print)9783030393212
DOIs
StatePublished - 2020
Event21st International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2020 - New Orleans, United States
Duration: 16 Jan 202021 Jan 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11990 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2020
Country/TerritoryUnited States
CityNew Orleans
Period16/01/2021/01/20

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