Automata Learning with an Incomplete but Inductive Teacher

2026-02-24

AI Summary

This work addresses the challenge of active learning when the target concept corresponds to a set of regular languages, as in regular language separation or inductive invariant synthesis, where non-uniqueness of solutions and incomplete teacher feedback hinder traditional approaches. The authors propose the IdMAT teacher formalism and the LIndA learning algorithm, which, for the first time, support queries admitting “unknown” responses and inductive facts. Uncertainty is uniformly modeled via SAT encoding, and the approach integrates incremental SAT solving with UNSAT core analysis. Inspired by Rivest and Schapire, it employs a counterexample minimization strategy that avoids case splitting. Experimental evaluation on a prototype implementation demonstrates the method’s effectiveness and scalability in both regular language separation and model checking tasks.

Technology Category

• Machine Learning: Active Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Active automata learning (AAL) under a Minimally Adequate Teacher (MAT) has been successfully used to infer a regular language through membership and equivalence queries. This language might not be fully characterized: we are then interested in finding any solution in a target class of possibly many regular languages. Some problems such as regular language separation or inductive invariant synthesis in the context of regular model checking (RMC) may indeed admit more than one answer. We therefore introduce IdMAT: a new teacher formalism answering queries with respect to any language in the target class, all at once. Such a teacher tailored towards invariant synthesis might provide incomplete"don't know"answers, but also inductive facts of the form"if w1 is accepted, so is w2". We pair IdMAT with a novel AAL algorithm LIndA that 1. encodes all uncertainties as a unique SAT instance and does not fork, 2. leverages incremental SAT solving and UNSAT core analysis, and 3. handles counterexamples of the simple or inductive type in a frugal manner inspired by the Rivest-Schapire refinement technique. We finally evaluate a prototype implementation in the context of regular language separation and RMC.

Problem

• automata learning
• incomplete teacher
• inductive invariant synthesis
• regular language separation
• regular model checking

Innovation

• active automata learning
• inductive teacher
• SAT-based learning
• regular model checking
• invariant synthesis