A Cegar-centric Bounded Reachability Analysis for Compositional Affine Hybrid Systems

2025-09-03

AI Summary

Addressing the dual challenges of semantic preservation and state-space explosion in bounded reachability analysis for compositional affine hybrid systems, this paper proposes a novel counterexample-guided abstraction refinement (CEGAR) framework. Instead of explicitly constructing the product automaton, our approach performs discrete abstract search to identify counterexamples and drives iterative state-space refinement. At the abstraction level, we employ step-wise compositional semantics to accelerate search; at the refinement level, we integrate shallow compositional semantics with symbolic reachability analysis. Continuous states are compactly represented via support functions, and intermediate results are cached for reuse. We implement the method in the tool SAT-Reach. Experimental evaluation demonstrates significant improvements in scalability and computational efficiency for compositional hybrid systems, providing a more practical and automated verification approach for complex hybrid systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Reachability analysis of compositional hybrid systems, where individual components are modeled as hybrid automata, poses unique challenges. In addition to preserving the compositional semantics while computing system behaviors, algorithms have to cater to the explosion in the number of locations in the parallel product automaton. In this paper, we propose a bounded reachability analysis algorithm for compositional hybrid systems with piecewise affine dynamics, based on the principle of counterexample guided abstraction refinement (CEGAR). In particular, the algorithm searches for a counterexample in the discrete abstraction of the composition model, without explicitly computing a product automaton. When a counterexample is discovered in the abstraction, its validity is verified by a refinement of the state-space guided by the abstract counterexample. The state-space refinement is through a symbolic reachability analysis, particularly using a state-of-the-art algorithm with support functions as the continuous state representation. In addition, the algorithm mixes different semantics of composition with the objective of improved efficiency. Step compositional semantics is followed while exploring the abstract (discrete) state-space, while shallow compositional semantics is followed during state-space refinement with symbolic reachability analysis. Optimizations such as caching the results of the symbolic reachability analysis, which can be later reused, have been proposed. We implement this algorithm in the tool SAT-Reach and demonstrate the scalability benefits.

Problem

• Bounded reachability analysis for compositional hybrid systems
• Avoiding explicit product automaton computation via CEGAR
• Mixing compositional semantics for improved efficiency

Innovation

• CEGAR-based abstraction refinement for compositional systems
• Symbolic reachability with support function representation
• Mixed compositional semantics for improved efficiency