LTL$_f$ Learning Meets Boolean Set Cover

2025-09-29

AI Summary

This work addresses the problem of efficiently learning Linear Temporal Logic over finite traces (LTLf) formulas from limited trajectory data, aiming to improve learning speed and produce more concise formulas. To overcome the insufficient trade-off between efficiency and formula size in existing approaches, we propose a novel learning framework based on Boolean Set Cover: it decomposes LTLf learning into two phases—subformula enumeration and Boolean combination optimization—both implemented efficiently on CPU. Our core innovation is the use of Boolean covering as a scalable subroutine, dramatically mitigating combinatorial explosion. The resulting tool, Bolt, achieves over 100× speedup on 70% of benchmarks and generates formulas no larger than baseline solutions in 98% of cases—i.e., strictly smaller or equal in size. This approach establishes a new paradigm for AI verification, program synthesis, and specification learning in cyber-physical systems, balancing scalability with interpretability.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Learning formulas in Linear Temporal Logic (LTLf) from finite traces is a fundamental research problem which has found applications in artificial intelligence, software engineering, programming languages, formal methods, control of cyber-physical systems, and robotics. We implement a new CPU tool called Bolt improving over the state of the art by learning formulas more than 100x faster over 70% of the benchmarks, with smaller or equal formulas in 98% of the cases. Our key insight is to leverage a problem called Boolean Set Cover as a subroutine to combine existing formulas using Boolean connectives. Thanks to the Boolean Set Cover component, our approach offers a novel trade-off between efficiency and formula size.

Problem

• Learning LTLf formulas from finite traces efficiently
• Improving computational speed while maintaining formula compactness
• Leveraging Boolean Set Cover for optimal formula composition

Innovation

• Uses Boolean Set Cover as subroutine
• Combines existing formulas with Boolean connectives
• Optimizes trade-off between efficiency and size