Symbolic Model Checking Using Intervals of Vectors

2026-02-03

Applications and Theory of Petri Nets

AI Summary

This work addresses the scalability bottleneck in symbolic model checking caused by state-space explosion by proposing a novel encoding method for Petri net markings based on vector intervals—distinct from conventional interval vectors—that supports global verification of CTL formulas. The approach innovatively introduces generalized vector intervals, defines their homomorphic operations and canonical forms, and thereby overcomes the expressiveness limitations of interval decision diagrams. By integrating saturation and clustering-based optimization techniques, the method achieves significant gains in verification efficiency. Empirical evaluation on the MCC 2022 benchmark suite demonstrates that the proposed technique substantially enhances both the scalability and performance of symbolic model checking.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Model checking is a powerful technique for software verification. However, the approach notably suffers from the infamous state space explosion problem. To tackle this, in this paper, we introduce a novel symbolic method for encoding Petri net markings. It is based on the use of generalised intervals on vectors, as opposed to existing methods based on vectors of intervals such as Interval Decision Diagrams. We develop a formalisation of these intervals, show that they possess homomorphic operations for model checking CTL on Petri nets, and define a canonical form that provides good performance characteristics. Our structure facilitates the symbolic evaluation of CTL formulas in the realm of global model checking, which aims to identify every state that satisfies a formula. Tests on examples of the model checking contest (MCC 2022) show that our approach yields promising results. To achieve this, we implement efficient computations based on saturation and clustering principles derived from other symbolic model checking techniques.

Problem

• state space explosion
• symbolic model checking
• Petri nets
• CTL
• global model checking

Innovation

• symbolic model checking
• generalised intervals on vectors
• Petri nets
• CTL
• state space explosion