Hybrid Spatiotemporal Logic for Automotive Applications: Modeling and Model-Checking

2026-03-25

AI Summary

This work addresses the lack of a unified formal verification framework capable of jointly characterizing spatial, temporal, and individual vehicle behaviors in highway autonomous driving. To this end, we propose Hybrid Spatio-Temporal Logic (HSTL), which uniquely integrates hybrid logic with spatio-temporal temporal logic to enable precise reference to specific vehicles and their historical trajectories. We formally define its semantics and develop a baseline model-checking algorithm along with two optimized variants that incorporate reachability-based state pruning and transition pruning to significantly enhance computational efficiency. Experimental evaluations on representative scenarios—including car-following, overtaking, intersection navigation, and platooning—demonstrate that the proposed optimizations achieve exponential performance gains over the baseline while effectively verifying critical safety properties.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We introduce a hybrid spatiotemporal logic for automotive safety applications (HSTL), focused on highway driving. Spatiotemporal logic features specifications about vehicles throughout space and time, while hybrid logic enables precise references to individual vehicles and their historical positions. We define the semantics of HSTL and provide a baseline model-checking algorithm for it. We propose two optimized model-checking algorithms, which reduce the search space based on the reachable states and possible transitions from one state to another. All three model-checking algorithms are evaluated on a series of common driving scenarios such as safe following, safe crossings, overtaking, and platooning. An exponential performance improvement is observed for the optimized algorithms.

Problem

• spatiotemporal logic
• automotive safety
• model checking
• hybrid logic
• formal verification

Innovation

• hybrid spatiotemporal logic
• model checking
• automotive safety
• reachable states
• state transition