We review the grammatical inference problem for regular languages which aims to generate a deterministic finite automaton from a representative set of training sample strings known to be in or not in the language. Although the general problem of producing a minimal DFA consistent with a given sample is known to be NP-hard, it is possible to generate minimal consistent DFA in polynomial time if certain constraints are satisfied by the given samples. In this work we propose a new algorithm which generates minimal DFA if the given training samples satisfy a certain sufficient condition. On the negative side, we also show that this problem is indeed hard, such that even for a more restricted class of training sets, the problem of generating minimal consistent DFA is already intractable.

中文翻译：

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来自样本字符串的最小一致 DFA

我们回顾了常规语言的语法推理问题，该问题旨在从已知在或不在该语言中的一组代表性训练样本字符串生成确定性有限自动机。尽管生成与给定样本一致的最小 DFA 的一般问题已知是 NP-hard，但如果给定样本满足某些约束，则可以在多项式时间内生成最小一致 DFA。在这项工作中，我们提出了一种新算法，如果给定的训练样本满足某个充分条件，则该算法会生成最小的 DFA。在消极方面，我们也表明这个问题确实很困难，以至于即使对于更受限制的训练集类别，生成最小一致 DFA 的问题也已经是棘手的。