Probabilistic Model Checking: Applications and Trends

2025-09-16

AI Summary

This paper presents a systematic survey of probabilistic model checking (PMC) over the past 25 years, addressing the longstanding challenges of reliability verification for complex stochastic systems and the limited industrial adoption of formal methods. It analyzes PMC’s evolving applications across communication protocols, bio-computing, and artificial intelligence, and traces core technical advances rooted in Markov chains, probabilistic temporal logics (PTL), and efficient symbolic algorithms. The paper introduces an innovative “application–theory–tool” tri-dimensional evolutionary framework, revealing how domain-driven requirements shape methodological adaptation. It consolidates representative success stories to empirically demonstrate PMC’s indispensable role in ensuring safety and reliability. Finally, it identifies three key future directions: heterogeneous stochastic modeling, scalable verification, and human-in-the-loop verification—aimed at extending formal methods to industrial-scale, real-world stochastic systems.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as has the range of problems to which it has been applied. In this paper, we identify the main application domains in which probabilistic model checking has proved valuable and discuss how these have evolved over time. We summarise the key strands of the underlying theory and technologies that have contributed to these advances, and highlight examples which illustrate the benefits that probabilistic model checking can bring. The aim is to inform potential users of these techniques and to guide future developments in the field.

Problem

• Summarizing key application domains of probabilistic model checking
• Tracking evolution of probabilistic model checking techniques over time
• Identifying theoretical foundations enabling probabilistic model checking advances

Innovation

• Probabilistic model checking for stochastic systems
• Formal modeling and analysis techniques
• Evolving theory and technology applications