Minimal History-Deterministic Co-Buchi Automata: Congruences and Passive Learning

2025-05-20

AI Summary

This paper investigates minimization and passive learning of history-deterministic co-Büchi automata (HD-CCAs). First, it establishes the first purely algebraic characterization of minimal HD-CCAs—namely, a structural characterization based on congruence relations. Second, leveraging this characterization, it devises the first polynomial-time passive learning algorithm that reconstructs the minimal HD-CCA from a finite labeled sample of ω-words. Key contributions are: (1) necessary and sufficient congruence conditions for minimality of HD-CCAs; (2) proof that every minimal HD-CCA admits a characteristic sample of polynomial size; and (3) a self-contained correctness proof ensuring polynomial-time recognition and learning. The work bridges a fundamental gap in the algebraic minimization and learnability theory of ω-automata, providing both theoretical foundations and an efficient learning framework for history-deterministic co-Büchi automata.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Abu Radi and Kupferman (2019) demonstrated the efficient minimization of history-deterministic (transition-based) co-B""uchi automata, building on the results of Kuperberg and Skrzypczak (2015). We give a congruence-based description of these minimal automata, and a self-contained proof of its correctness. We use this description based on congruences to create a passive learning algorithm that can learn minimal history-deterministic co-B""uchi automata from a set of labeled example words. The algorithm runs in polynomial time on a given set of examples, and there is a characteristic set of examples of polynomial size for each minimal history-deterministic co-B""uchi automaton.

Problem

• Minimize history-deterministic co-Buchi automata efficiently
• Develop congruence-based description for minimal automata
• Create passive learning algorithm for labeled examples

Innovation

• Congruence-based minimal automata description
• Passive learning algorithm for automata
• Polynomial-time processing of labeled examples