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arXiv · 2509.24347

Efficient Decomposition Identification of Deterministic Finite Automata from Examples

Junjie Meng·Jie An·Yong Li·Andrea Turrini·Fanjiang Xu·Naijun Zhan·Miaomiao Zhang
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Abstract

The identification of deterministic finite automata (DFAs) from labeled examples is a cornerstone of automata learning, yet traditional methods focus on learning monolithic DFAs, which often yield a large DFA lacking simplicity and interoperability. Recent work addresses these limitations by exploring DFA decomposition identification problems (DFA-DIPs), which model system behavior as intersections of multiple DFAs, offering modularity for complex tasks. However, existing DFA-DIP approaches depend on SAT encodings derived from Augmented Prefix Tree Acceptors (APTAs), incurring scalability limitations due to their inherent redundancy. In this work, we advance DFA-DIP research through studying two variants: the traditional Pareto-optimal DIP and the novel states-optimal DIP, which prioritizes a minimal number of states. We propose a novel framework that bridges DFA decomposition with recent advancements in automata representation. One of our key innovations replaces APTA with 3-valued DFA (3DFA) derived directly from labeled examples. This compact representation eliminates redundancies of APTA, thus drastically reducing variables in the improved SAT encoding. Experimental results demonstrate that our 3DFA-based approach achieves significant efficiency gains for the Pareto-optimal DIP while enabling a scalable solution for the states-optimal DIP.

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Junjie Meng, Jie An, Yong Li, Andrea Turrini, Fanjiang Xu, Naijun Zhan, Miaomiao Zhang. 2025-10-12. Efficient Decomposition Identification of Deterministic Finite Automata from Examples. https://arxiv.org/abs/2509.24347

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