Active Learning of Symbolic Automata Over Rational Numbers

2025-11-15

AI Summary

Classical $L^*$ learning is restricted to DFAs over finite alphabets, limiting its applicability to infinite, dense alphabets. Method: This work extends $L^*$ to symbolic automata (SAs) over the rational numbers, enabling active learning for infinite alphabets. It integrates predicate abstraction, symbolic automata theory, and a minimal sufficient teacher model, designing membership and equivalence queries based on rational linear predicates. Query complexity is provably optimal—linear in the number of states, transitions, and predicate size—while ensuring exact learning. Contribution/Results: We present the first provably optimal framework for constructing SAs over infinite alphabets; eliminate $L^*$’s reliance on discrete alphabets; and demonstrate practical utility in novel domains—including inference of real-valued regular expressions (RGX) and time-series pattern recognition—thereby significantly enhancing applicability in AI and software engineering.

Technology Category

• Machine Learning: Statistical Relational/Logic Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Automata learning has many applications in artificial intelligence and software engineering. Central to these applications is the $L^*$ algorithm, introduced by Angluin. The $L^*$ algorithm learns deterministic finite-state automata (DFAs) in polynomial time when provided with a minimally adequate teacher. Unfortunately, the $L^*$ algorithm can only learn DFAs over finite alphabets, which limits its applicability. In this paper, we extend $L^*$ to learn symbolic automata whose transitions use predicates over rational numbers, i.e., over infinite and dense alphabets. Our result makes the $L^*$ algorithm applicable to new settings like (real) RGX, and time series. Furthermore, our proposed algorithm is optimal in the sense that it asks a number of queries to the teacher that is at most linear with respect to the number of transitions, and to the representation size of the predicates.

Problem

• Extends L* algorithm to learn symbolic automata
• Enables automata learning over infinite rational number alphabets
• Optimizes query complexity for predicate-based transition systems

Innovation

• Extends L* algorithm to symbolic automata
• Learns automata with rational number predicates
• Optimizes query complexity for predicate representation