Symmetric Proofs of Parameterized Programs

2026-01-26

AI Summary

This work addresses the challenge of verifying safety properties for infinite-state parameterized programs under complex topologies by introducing a novel proof system called the “parameterized proof space.” Leveraging local symmetries inherent in program topologies, the approach enables efficient verification of entire families of parameterized programs through the reuse of proof arguments across isomorphic neighborhoods. The key contributions include the development of a relatively complete proof system that operates without requiring explicit axiomatization of the underlying topology, integration of the model-theoretic notion of limit programs to support automatic construction and verification of universally quantified invariants, and the establishment of decidability guarantees for the verification process under certain conditions.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying symmetry in such programs. This is a local notion of symmetry which enables the proof system to reuse proof arguments for isomorphic neighbourhoods in program topologies. We prove a sophisticated relative completeness result for the proof system with respect to a class of universally quantified invariants. We also investigate the problem of algorithmic construction of these proofs. We present a construction, inspired by classic results in model theory, where an infinitary limit program can be soundly and completely verified in place of the parameterized family, under some conditions. Furthermore, we demonstrate how these proofs can be constructed and checked against these programs without the need for axiomatization of the underlying topology for proofs or the programs. Finally, we present conditions under which our algorithm becomes a decision procedure.

Problem

• parameterized programs
• safety verification
• infinite-state systems
• symmetry
• program topologies

Innovation

• parametric proof spaces
• symmetry
• parameterized programs
• relative completeness
• infinitary limit program