Property-directed inference of universal invariants or proving their absence

A. Karbyshev*, N. Bjørner, S. Itzhaky, N. Rinetzky, S. Shoham

*Corresponding author for this work

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

23 Scopus citations


We present Universal Property Directed Reachability (PDR), a property-directed procedure for automatic inference of invariants in a universal fragment of first-order logic. PDR is an extension of Bradley’s PDR/IC3 algorithm for inference of propositional invariants. PDR terminates when it either discovers a concrete counterexample, infers an inductive universal invariant strong enough to establish the desired safety property, or finds a proof that such an invariant does not exist. We implemented an analyzer based on PDR, and applied it to a collection of list-manipulating programs. Our analyzer was able to automatically infer universal invariants strong enough to establish memory safety and certain functional correctness properties, show the absence of such invariants for certain natural programs and specifications, and detect bugs. All this, without the need for user-supplied abstraction predicates.

Original languageEnglish
Title of host publicationComputer Aided Verification - 27th International Conference, CAV 2015, Proceedings
EditorsCorina S. Pasareanu, Daniel Kroening, Corina S. Pasareanu, Daniel Kroening
PublisherSpringer Verlag
Number of pages20
ISBN (Print)9783319216898, 9783319216898
StatePublished - 2015
Event27th International Conference on Computer Aided Verification, CAV 2015 - San Francisco, United States
Duration: 18 Jul 201524 Jul 2015

Publication series

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


Conference27th International Conference on Computer Aided Verification, CAV 2015
Country/TerritoryUnited States
CitySan Francisco


FundersFunder number
European Research Council
Seventh Framework ProgrammeFP7/2007-2013
United States-Israel Binational Science Foundation
Broadcom Foundation
European Research Council321174-VSSC
United States-Israel Binational Science Foundation2012259
Tel Aviv University
Seventh Framework Programme308830


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