Counterexample-Guided Abstraction Refinement for Generalized Graph Transformation Systems (Full Version)

2025-04-11

AI Summary

This paper addresses the (un)reachability verification problem between initial and error states in graph transformation systems specified by first-order nested conditions. Due to infinite state spaces, this problem is generally undecidable. To tackle it, we propose the first Counterexample-Guided Abstraction Refinement (CEGAR) framework tailored for general graph transformation systems with first-order nested condition constraints, integrating abstract interpretation, predicate abstraction, and graph transformation semantics into a terminating automated verification procedure. Our key contribution is a novel abstraction and refinement mechanism specifically designed for nested conditions, enabling precise unreachability proofs for complex, structured error states. We validate the effectiveness and practicality of our approach on multiple case studies. The method provides a new, generic pathway for formal verification of reactive systems governed by structural constraints.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

This paper addresses the following verification task: Given a graph transformation system and a class of initial graphs, can we guarantee (non-)reachability of a given other class of graphs that characterizes bad or erroneous states? Both initial and bad states are characterized by nested conditions (having first-order expressive power). Such systems typically have an infinite state space, causing the problem to be undecidable. We use abstract interpretation to obtain a finite approximation of that state space, and employ counter-example guided abstraction refinement to iteratively obtain suitable predicates for automated verification. Although our primary application is the analysis of graph transformation systems, we state our result in the general setting of reactive systems.

Problem

• Verifying graph reachability in transformation systems
• Handling infinite state spaces via abstraction refinement
• Ensuring automated verification of nested conditions

Innovation

• Abstract interpretation for finite state approximation
• Counter-example guided abstraction refinement
• Automated verification with nested conditions