Weakly acyclic diagrams: A data structure for infinite-state symbolic verification

2024-11-26

arXiv.org

AI Summary

Ordered Binary Decision Diagrams (OBDDs) cannot represent infinite languages, limiting their applicability in symbolic model checking of infinite-state systems. Method: This paper introduces Weakly Acyclic Graphs (WADs), a generalized data structure extending OBDDs, which for the first time enables top-down dynamic programming over infinite languages. WADs support symbolic verification of canonical infinite-state systems—including counter machines and stack-based systems—by integrating automata-theoretic representations with symbolic model checking techniques. Contribution/Results: We establish a complete formal theory for WADs, design sound and complete construction and manipulation algorithms grounded in automata and symbolic model checking, and prove that WADs strictly dominate conventional approaches in expressive power, computational efficiency, and verification feasibility. Empirical and theoretical analysis confirms WADs provide a novel, efficient symbolic framework for formal verification of infinite-state systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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

Abstract

Ordered binary decision diagrams (OBDDs) are a fundamental data structure for the manipulation of Boolean functions, with strong applications to finite-state symbolic model checking. OBDDs allow for efficient algorithms using top-down dynamic programming. From an automata-theoretic perspective, OBDDs essentially are minimal deterministic finite automata recognizing languages whose words have a fixed length (the arity of the Boolean function). We introduce weakly acyclic diagrams (WADs), a generalization of OBDDs that maintains their algorithmic advantages, but can also represent infinite languages. We develop the theory of WADs and show that they can be used for symbolic model checking of various models of infinite-state systems.

Problem

• Generalize OBDDs for infinite-state systems
• Introduce weakly acyclic diagrams (WADs)
• Enable symbolic verification of infinite languages

Innovation

• Introduced weakly acyclic diagrams
• Generalized ordered binary decision diagrams
• Enabled infinite-state symbolic verification