Learning Deterministic Finite-State Machines from the Prefixes of a Single String is NP-Complete
arXiv:2601.12621v2 Announce Type: replace-cross Abstract: It is well known that computing a minimum deterministic finite automaton consistent with a given set of positive and negative examples is NP-hard. Previous work has identified conditions on the input sample under which the problem becomes tractable or remains hard. In this paper, we study the computational complexity of the case where the input sample is prefix-closed. This formulation is equivalent to computing a minimum Moore machine consistent with observations along its runs. We show that the problem is NP-hard to approximate when t
The proliferation of AI and autonomous systems is driving renewed interest in the theoretical underpinnings of machine learning, especially regarding the complexity of learning minimal representations.
This research highlights fundamental computational limits in learning deterministic finite-state machines, critical for developing efficient and robust AI agents and formal verification systems.
The understanding of the inherent difficulty in certain machine learning problems is refined, suggesting where classical computational complexity theory still presents significant hurdles for practical AI applications.
- · Theoretical computer scientists
- · Researchers focused on efficient algorithm design
- · Developers of specialized AI architectures
- · Researchers seeking general-purpose, 'easy' solutions for sequential learning
- · Companies relying on brute-force approaches for complex learning tasks
This finding indicates that certain types of 'learning from example' problems in AI are inherently hard, even under seemingly simplifying conditions.
It may drive the development of more constrained learning environments or novel heuristic approaches to circumvent NP-completeness in practical AI agent design.
The identified limits could indirectly influence the focus of AI research towards areas where tractable solutions are more readily achievable, or towards architectures that intrinsically sidestep these complexities.
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Read at arXiv cs.LG