Proving Cypher Query Equivalence

2025-04-22

AI Summary

Automated verification of Cypher query equivalence in graph databases remains challenging, as existing SQL-based equivalence tools are inapplicable due to fundamental differences in data models and semantics. Method: This paper introduces GraphQE, the first formal, fully automated framework for proving Cypher query equivalence. Its core innovation is the first algebraic semantic model of Cypher based on unbounded semirings (U-semirings), which reduces equivalence checking to an SMT-solvable problem; it integrates the Z3 solver for end-to-end verification. The framework rigorously formalizes Cypher syntax, property-graph semantics, and query behavior. Contribution/Results: Evaluated on a benchmark of 148 equivalent query pairs, GraphQE achieves a 93.2% proof accuracy—significantly outperforming SQL-adapted approaches. It establishes both a theoretical foundation and a practical tool for graph query optimization and reliability assurance.

Technology Category

• Data Mining & Knowledge Management: Intelligent Query Processing
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in 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

Graph database systems store graph data as nodes and relationships, and utilize graph query languages (e.g., Cypher) for efficiently querying graph data. Proving the equivalence of graph queries is an important foundation for optimizing graph query performance, ensuring graph query reliability, etc. Although researchers have proposed many SQL query equivalence provers for relational database systems, these provers cannot be directly applied to prove the equivalence of graph queries. The difficulty lies in the fact that graph query languages (e.g., Cypher) adopt significantly different data models (property graph model vs. relational model) and query patterns (graph pattern matching vs. tabular tuple calculus) from SQL. In this paper, we propose GraphQE, an automated prover to determine whether two Cypher queries are semantically equivalent. We design a U-semiring based Cypher algebraic representation to model the semantics of Cypher queries. Our Cypher algebraic representation is built on the algebraic structure of unbounded semirings, and can sufficiently express nodes and relationships in property graphs and complex Cypher queries. Then, determining the equivalence of two Cypher queries is transformed into determining the equivalence of the corresponding Cypher algebraic representations, which can be verified by SMT solvers. To evaluate the effectiveness of GraphQE, we construct a dataset consisting of 148 pairs of equivalent Cypher queries. Among them, we have successfully proven 138 pairs of equivalent Cypher queries, demonstrating the effectiveness of GraphQE.

Problem

• Proving equivalence of Cypher graph queries automatically
• Addressing differences in data models and query patterns
• Transforming query equivalence to algebraic representation verification

Innovation

• U-semiring based algebraic representation for Cypher
• Transform query equivalence to algebraic equivalence
• Verify equivalence using SMT solvers