Regular language inference, initiated by Angluin, has many developments, including applications in software engineering and testing. However, the capability of finite automata to model the system data is quite limited and, in many cases, extended finite state machine formalisms, that combine the system control with data structures, are used instead. The application of Angluin-style inference algorithms to extended state machines would involve constructing a minimal deterministic extended finite state machine consistent with a deterministic 3-valued deterministic finite automaton. In addition to the usual, accepting and rejecting, states of finite automaton, a 3-valued deterministic finite automaton may have “don't care” states; the sequences of inputs that reach such states may be considered as accepted or rejected, as is convenient. The aforementioned construction reduces to finding a minimal deterministic finite automaton consistent with a 3-valued deterministic finite automaton, that preserves the deterministic nature of the extended model that also handles the data structure associated with it. This paper investigates fundamental properties of extended finite state machines in relation to Angluin's language inference problem and provides an inference algorithm for such models.

由Angluin发起的常规语言推理具有许多发展，包括软件工程和测试中的应用。但是，有限自动机对系统数据进行建模的能力非常有限，在许多情况下，使用了将系统控制与数据结构结合起来的扩展有限状态机形式主义。Angluin风格的推理算法在扩展状态机上的应用将涉及构造与确定性三值确定性有限自动机一致的最小确定性扩展有限状态机。除了通常的有限自动机的接受和拒绝状态外，三值确定性有限自动机可能还具有“无关”状态。为了方便，可以将达到这种状态的输入序列视为接受或拒绝。前述构造简化为找到与三值确定性有限自动机一致的最小确定性有限自动机，其保留了扩展模型的确定性，该扩展模型还处理与之关联的数据结构。本文研究了与Angluin语言推理问题有关的扩展有限状态机的基本特性，并为此类模型提供了一种推理算法。