Quantifiers on Demand

Arie Gurfinkel*, Sharon Shoham, Yakir Vizel

*Corresponding author for this work

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

24 Scopus citations


Automated program verification is a difficult problem. It is undecidable even for transition systems over Linear Integer Arithmetic (LIA). Extending the transition system with theory of Arrays, further complicates the problem by requiring inference and reasoning with universally quantified formulas. In this paper, we present a new algorithm, Quic3, that extends IC3 to infer universally quantified invariants over the combined theory of LIA and Arrays. Unlike other approaches that use either IC3 or an SMT solver as a black box, Quic3 carefully manages quantified generalization (to construct quantified invariants) and quantifier instantiation (to detect convergence in the presence of quantifiers). While Quic3 is not guaranteed to converge, it is guaranteed to make progress by exploring longer and longer executions. We have implemented Quic3 within the Constrained Horn Clause solver engine of Z3 and experimented with it by applying Quic3 to verifying a variety of public benchmarks of array manipulating C programs.

Original languageEnglish
Title of host publicationAutomated Technology for Verification and Analysis - 16th International Symposium, ATVA 2018, Proceedings
EditorsChao Wang, Shuvendu K. Lahiri
PublisherSpringer Verlag
Number of pages19
ISBN (Print)9783030010898
StatePublished - 2018
Event16th International Symposium on Automated Technology for Verification and Analysis, ATVA 2018 - Los Angeles, United States
Duration: 7 Oct 201810 Oct 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11138 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Symposium on Automated Technology for Verification and Analysis, ATVA 2018
Country/TerritoryUnited States
CityLos Angeles


FundersFunder number
Bloom's Syndrome Foundation2016260, 2012259
Canadian Friends of Tel Aviv University
Horizon 2020 Framework Programme759102
Blavatnik Family Foundation
Natural Sciences and Engineering Research Council of CanadaRGPAS-2017-507912
European Research Council
United States-Israel Binational Science Foundation


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