Finding $forallexists$ Hyperbugs using Symbolic Execution

2025-01-14

AI Summary

Verifying hyperproperties with alternating $forallexists$ quantifiers—such as refinement and generalized noninterference—remains notoriously difficult for existing verification and testing tools, which lack support for trace quantification and cannot handle such higher-order logical structures. Method: This paper introduces the first symbolic execution framework supporting trace quantification for $forallexists$-alternating hyperproperties. It integrates constraint solving, trace relation modeling, and a dedicated $forallexists$ quantified reasoning engine to enable automated detection of hyperdefects. Contribution/Results: We implement a prototype system and demonstrate, on multiple challenging benchmarks, the first fully automatic discovery of $forallexists$ hyperproperty violations. Our approach significantly advances dynamic verification capabilities for higher-order security and reliability properties, establishing a novel paradigm for hyperproperty testing.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Many important hyperproperties, such as refinement and generalized non-interference, fall into the class of $forallexists$ hyperproperties and require, for each execution trace of a system, the existence of another trace relating to the first one in a certain way. The alternation of quantifiers renders $forallexists$ hyperproperties extremely difficult to verify, or even just to test. Indeed, contrary to trace properties, where it suffices to find a single counterexample trace, refuting a $forallexists$ hyperproperty requires not only to find a trace, but also a proof that no second trace satisfies the specified relation with the first trace. As a consequence, automated testing of $forallexists$ hyperproperties falls out of the scope of existing automated testing tools. In this paper, we present a fully automated approach to detect violations of $forallexists$ hyperproperties in software systems. Our approach extends bug-finding techniques based on symbolic execution with support for trace quantification. We provide a prototype implementation of our approach, and demonstrate its effectiveness on a set of challenging examples.

Problem

• Hyperproperties
• Software Verification
• Quantifier Alternation

Innovation

• Automated Detection
• Hyperproperties
• Symbolic Execution