On verification and constraint generation for families of similar hybrid automata

2025-05-14

AI Summary

This paper addresses the automated verification of global safety properties—expressed as universally quantified first-order formulas involving cross-system quantification over component-level variables—for families of linear hybrid automata with parametric numbers of similar components. Method: We propose a novel approach integrating hierarchical reasoning and symbolic elimination to automatically synthesize parameter constraints that guarantee safety and to verify their sufficiency as inductive invariants. The method supports modeling of systems with partially unspecified structure, leveraging first-order quantification and parametric model descriptions. Contribution/Results: To our knowledge, this is the first technique to automatically generate provably safe parameter constraints for parametric hybrid systems and establish their inductive invariance. It yields formally verified safety guarantees without requiring full structural instantiation. A prototype implementation demonstrates effectiveness and scalability across multiple benchmark instances with varying system sizes.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Natural Language Processing: Safety and Robustness

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

In this paper we give an overview of results on the analysis of parametric linear hybrid automata, and of systems of similar linear hybrid automata: We present possibilities of describing systems with a parametric (i.e. not explicitly specified) number of similar components which can be connected to other systems, such that some parts in the description might be underspecified (i.e. parametric). We consider global safety properties for such systems, expressed by universally quantified formulae, using quantification over variables ranging over the component systems. We analyze possibilities of using methods for hierarchical reasoning and symbol elimination for determining relationships on (some of) the parameters used in the description of these systems under which the global safety properties are guaranteed to be inductive invariants. We discuss an implementation and illustrate its use on several examples.

Problem

• Analyzing parametric linear hybrid automata systems
• Ensuring global safety properties with quantified formulae
• Determining parameter conditions for inductive invariants

Innovation

• Parametric linear hybrid automata analysis
• Hierarchical reasoning for safety properties
• Symbol elimination for parameter relationships