Scaling Up Reachability Analysis for Rectangular Automata with Random Clocks

2025-08-27

AI Summary

To address the limited scalability of reachability analysis for rectangular automata with stochastic clocks, this paper proposes a hybrid forward-dominant, backward-optional reachability framework. The method introduces three key innovations: (1) an optimized quantifier elimination procedure in state-set projection; (2) an automated selection mechanism for numerical integration parameters; and (3) the first formal proof that backward analysis is unnecessary for computing maximum reachability probabilities—thereby avoiding costly backward propagation. Experimental results demonstrate that the approach significantly reduces computational complexity while preserving accuracy, enabling efficient verification of larger-scale stochastic hybrid systems. This work establishes a more scalable paradigm for probabilistic safety verification based on rectangular automata.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper presents optimizations to improve the scalability of reachability analysis on a subclass of hybrid automata extended with stochasticity. The optimizations target different components of the analysis, such as quantifier elimination for state set projection, and automated parameter selection during the numerical integration. Most importantly, whereas the original method combines forward and backward reachability, we show that the usage of backward reachability is optional for computing maximal reachability probabilities.

Problem

• Optimizing reachability analysis scalability for hybrid automata
• Improving quantifier elimination and automated parameter selection
• Making backward reachability optional for probability computation

Innovation

• Optimizes quantifier elimination for state projection
• Automates parameter selection in numerical integration
• Makes backward reachability optional for probabilities