Hyperproperty Verification as CHC Satisfiability

Shachar Itzhaky*, Sharon Shoham, Yakir Vizel

*Corresponding author for this work

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

Abstract

Hyperproperties specify the behavior of a system across multiple executions, and are an important extension of regular temporal properties. So far, such properties have resisted comprehensive treatment by software model-checking approaches such as IC3/PDR, due to the need to find not only an inductive invariant but also a total alignment of different executions that facilitates simpler inductive invariants. We show how this treatment is achieved via a reduction from the verification problem of ∀ hyperproperties to Constrained Horn Clauses (CHCs). Our starting point is a set of universally quantified formulas in first-order logic (modulo theories) that encode the verification of ∀ hyperproperties over infinite-state transition systems. The first-order encoding uses uninterpreted predicates to capture the (1) witness function for existential quantification over traces, (2) alignment of executions, and (3) corresponding inductive invariant. Such an encoding was previously proposed for k-safety properties. Unfortunately, finding a satisfying model for the resulting first-order formulas is beyond reach for modern first-order satisfiability solvers. Previous works tackled this obstacle by developing specialized solvers for the aforementioned first-order formulas. In contrast, we show that the same problems can be encoded as CHCs and solved by existing CHC solvers. CHC solvers take advantage of the unique structure of CHC formulas and handle the combination of quantifiers with theories and uninterpreted predicates more efficiently. Our key technical contribution is a logical transformation of the aforementioned sets of first-order formulas to equi-satisfiable sets of CHCs. The transformation to CHCs is sound and complete, and applying it to the first-order formulas that encode verification of hyperproperties leads to a CHC encoding of these problems. We implemented the CHC encoding in a prototype tool and show that, using existing CHC solvers for solving the CHCs, the approach already outperforms state-of-the-art tools for hyperproperty verification by orders of magnitude.

Original languageEnglish
Title of host publicationProgramming Languages and Systems - 33rd European Symposium on Programming, ESOP 2024, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024, Proceedings
EditorsStephanie Weirich
PublisherSpringer Science and Business Media Deutschland GmbH
Pages212-241
Number of pages30
ISBN (Print)9783031572661
DOIs
StatePublished - 2024
Event33rd European Symposium on Programming, ESOP 2024, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024 - Luxembourg City, Luxembourg
Duration: 6 Apr 202411 Apr 2024

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14577 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference33rd European Symposium on Programming, ESOP 2024, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024
Country/TerritoryLuxembourg
CityLuxembourg City
Period6/04/2411/04/24

Funding

FundersFunder number
European Research Council
Horizon 2020 Framework Programme759102-SVIS
Horizon 2020 Framework Programme
Israel Science Foundation2117/23, 2875/21
Israel Science Foundation
NSF-BSF2018675

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