Automata learning: from probabilistic to quantum

Doctoral Thesis

This thesis advances automata learning, a key area in computer science, with applications in software verification, biological analysis, and autonomous technologies. It explores three main themes: first, it introduces a passive learning algorithm for generating compact probabilistic models from positive samples, improving accuracy with larger sample sizes. Second, the research investigates the independent learning of structural and probabilistic components in non-deterministic probabilistic automata, using both positive and negative samples for enhanced modeling. Third, the thesis focuses on active learning techniques for deterministic and weighted automata, extending the Hankel matrix method to probabilistic and quantum automata. The thesis also proposes an active learning algorithm for quantum automata, integrating nonlinear optimization and matrix analysis to improve language modeling in quantum applications. The research concludes with an implementation of quantum automata in...Show moreThis thesis advances automata learning, a key area in computer science, with applications in software verification, biological analysis, and autonomous technologies. It explores three main themes: first, it introduces a passive learning algorithm for generating compact probabilistic models from positive samples, improving accuracy with larger sample sizes. Second, the research investigates the independent learning of structural and probabilistic components in non-deterministic probabilistic automata, using both positive and negative samples for enhanced modeling. Third, the thesis focuses on active learning techniques for deterministic and weighted automata, extending the Hankel matrix method to probabilistic and quantum automata. The thesis also proposes an active learning algorithm for quantum automata, integrating nonlinear optimization and matrix analysis to improve language modeling in quantum applications. The research concludes with an implementation of quantum automata in optical experiments, enabling dynamic input encoding and overcoming previous limitations. These advancements lay the groundwork for future developments in probabilistic modeling and quantum computing.
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Probabilistic models

Active learning

Passive learning

Quantum automata

Quantum optical experiments

Non-deterministic probabilistic automata

Deterministic finite automata