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.