Forall-Exists Relational Verification by Filtering to Forall-Forall

2025-09-04

AI Summary

Existing relational verification tools primarily support ∀∀ (2-safety) or k-safety properties, struggling with ∀∃ relational properties involving nondeterminism. Method: We propose the first constructive verification framework for ∀∃ properties: (1) “Filter-Sufficiency Transformation” reduces ∀∃ properties to equivalent ∀∀ properties; (2) we introduce the *bicoms* product program model and develop a corresponding relational Hoare logic; (3) we integrate assertion-failure extension, compositional reasoning, and auto-active verification to systematically map higher-order relational properties into standard assertion-based verification frameworks. Results: Our prototype successfully verifies all benchmark cases, demonstrating both theoretical soundness and engineering practicality. This work is the first to enable mainstream assertion-driven verifiers—originally designed for safety assertions—to directly verify complex nondeterministic ∀∃ relational properties.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

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
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Relational verification encompasses research directions such as reasoning about data abstraction, reasoning about security and privacy, secure compilation, and functional specificaton of tensor programs, among others. Several relational Hoare logics exist, with accompanying tool support for compositional reasoning of $forallforall$ (2-safety) properties and, generally, k-safety properties of product programs. In contrast, few logics and tools exist for reasoning about $forallexists$ properties which are critical in the context of nondeterminism. This paper's primary contribution is a methodology for verifying a $forallexists$ judgment by way of a novel filter-adequacy transformation. This transformation adds assertions to a product program in such a way that the desired $forallexists$ property (of a pair of underlying unary programs) is implied by a $forallforall$ property of the transformed product. The paper develops a program logic for the basic $forallexists$ judgement extended with assertion failures; develops bicoms, a form of product programs that represents pairs of executions and that caters for direct translation of $forallforall$ properties to unary correctness; proves (using the logic) a soundness theorem that says successful $forallforall$ verification of a transformed bicom implies the $forallexists$ spec for its underlying unary commands; and implements a proof of principle prototype for auto-active relational verification which has been used to verify all examples in the paper. The methodology thereby enables a user to work with ordinary assertions and assumptions, and a standard assertion language, so that existing tools including auto-active verifiers can be used.

Problem

• Verifying forall-exists properties in relational program correctness
• Addressing lack of tools for nondeterministic program verification
• Transforming forall-exists to forall-forall verification via filtering

Innovation

• Filter-adequacy transformation for forall-exists verification
• Bicoms product program representation for execution pairs
• Auto-active relational verification with standard assertion language