Invariant Inference with Provable Complexity from the Monotone Theory

Yotam M.Y. Feldman*, Sharon Shoham

*Corresponding author for this work

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

Abstract

Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity of such algorithms are scarce, and limited to simple syntactic forms of invariants. In this paper we achieve invariant inference algorithms, in the domain of propositional transition systems, with provable upper bounds on the number of SAT calls. We do this by building on the monotone theory, developed by Bshouty for exact learning Boolean formulas. We prove results for two invariant inference frameworks: (i) model-based interpolation, where we show an algorithm that, under certain conditions about reachability, efficiently infers invariants when they have both short CNF and DNF representations (transcending previous results about monotone invariants); and (ii) abstract interpretation in a domain based on the monotone theory that was previously studied in relation to property-directed reachability, where we propose an efficient implementation of the best abstract transformer, leading to overall complexity bounds on the number of SAT calls. These results build on a novel procedure for computing least monotone overapproximations.

Original languageEnglish
Title of host publicationStatic Analysis - 29th International Symposium, SAS 2022, Proceedings
EditorsGagandeep Singh, Caterina Urban
PublisherSpringer Science and Business Media Deutschland GmbH
Pages201-226
Number of pages26
ISBN (Print)9783031223075
DOIs
StatePublished - 2022
Event29th International Static Analysis Symposium, SAS 2022 - Auckland, New Zealand
Duration: 5 Dec 20227 Dec 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13790 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference29th International Static Analysis Symposium, SAS 2022
Country/TerritoryNew Zealand
CityAuckland
Period5/12/227/12/22

Funding

FundersFunder number
Horizon 2020 Framework Programme759102-SVIS
European Research Council
Israel Science Foundation1810/18

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