Verifying Parameterized Networks Specified by Vertex-Replacement Graph Grammars

2025-05-02

AI Summary

This paper addresses the Parameterized Reachability Problem (PRP) for networks parameterized by Vertex-Replacement graph grammars (VR), where nodes execute finite-state processes and communicate via binary handshaking. We propose a sound, complete, and decidable reduction: dense parametric topologies—such as cliques and complete multipartite graphs—described by VR grammars are systematically transformed into Hyperedge-Replacement (HR) graph grammars augmented with routing edges. This transformation establishes, for the first time, semantic equivalence between VR and HR formalisms for parameterized verification, enabling direct application of existing HR-based verification tools to VR-defined networks without requiring new analysis frameworks. Our key contribution is extending HR-based verification beyond its traditional reliance on sparse graph structures, thereby supporting high-density parametric architectures. This significantly broadens the applicability and practical utility of formal verification techniques for complex, scalable network systems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

We consider the parametric reachability problem (PRP) for families of networks described by vertex-replacement (VR) graph grammars, where network nodes run replicas of finite-state processes that communicate via binary handshaking. We show that the PRP problem for VR grammars can be effectively reduced to the PRP problem for hyperedge-replacement (HR) grammars at the cost of introducing extra edges for routing messages. This transformation is motivated by the existence of several parametric verification techniques for families of networks specified by HR grammars, or similar inductive formalisms. Our reduction enables applying the verification techniques for HR systems to systems with dense architectures, such as user-specified cliques and multi-partite graphs.

Problem

• Verifying reachability in networks defined by vertex-replacement grammars
• Reducing vertex-replacement PRP to hyperedge-replacement PRP
• Enabling verification for dense architectures like cliques

Innovation

• Reduces VR grammars to HR grammars
• Introduces extra edges for routing
• Enables verification for dense architectures