Inferring Invariants with Quantifier Alternations: Taming the Search Space Explosion

Jason R. Koenig*, Oded Padon, Sharon Shoham, Alex Aiken

*Corresponding author for this work

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

6 Scopus citations

Abstract

We present a PDR/IC3 algorithm for finding inductive invariants with quantifier alternations. We tackle scalability issues that arise due to the large search space of quantified invariants by combining a breadth-first search strategy and a new syntactic form for quantifier-free bodies. The breadth-first strategy prevents inductive generalization from getting stuck in regions of the search space that are expensive to search and focuses instead on lemmas that are easy to discover. The new syntactic form is well-suited to lemmas with quantifier alternations by allowing both limited conjunction and disjunction in the quantifier-free body, while carefully controlling the size of the search space. Combining the breadth-first strategy with the new syntactic form results in useful inductive bias by prioritizing lemmas according to: (i) well-defined syntactic metrics for simple quantifier structures and quantifier-free bodies, and (ii) the empirically useful heuristic of preferring lemmas that are fast to discover. On a benchmark suite of primarily distributed protocols and complex Paxos variants, we demonstrate that our algorithm can solve more of the most complicated examples than state-of-the-art techniques.

Original languageEnglish
Title of host publicationTools and Algorithms for the Construction and Analysis of Systems - 28th International Conference, TACAS 2022, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022, Proceedings
EditorsDana Fisman, Grigore Rosu
PublisherSpringer Science and Business Media Deutschland GmbH
Pages338-356
Number of pages19
ISBN (Print)9783030995232
DOIs
StatePublished - 2022
Event28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022 held as part of 25th European Joint Conferences on Theory and Practice of Software, ETAPS 2022 - Munich, Germany
Duration: 2 Apr 20227 Apr 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13243 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022 held as part of 25th European Joint Conferences on Theory and Practice of Software, ETAPS 2022
Country/TerritoryGermany
CityMunich
Period2/04/227/04/22

Funding

FundersFunder number
National Science FoundationCCF-1160904, CCF-1409813
Bonfils-Stanton Foundation2016260
Horizon 2020 Framework Programme759102
Israel Science Foundation1810/18

    Keywords

    • PDR/IC3
    • invariant inference
    • quantifier alternation

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