<p>Inferring protocol state machines from observable information presents a significant challenge in protocol reverse engineering (PRE), especially when passively collected traffic suffers from message loss, resulting in an incomplete protocol state space. This paper introduces an innovative method for actively inferring protocol state machines using the minimally adequate teacher (MAT) framework. By incorporating session completion and deterministic mutation techniques, this method broadens the range of protocol messages, thereby constructing a more comprehensive input space for the protocol state machine from an incomplete message domain. Additionally, the efficiency of active inference is improved through several optimizations for the <i>L</i><Stack> _M ⁺ </Stack> algorithm, including traffic deduplication, the construction of an expanded prefix tree acceptor (EPTA), query optimization based on responses, and random counterexample generation. Experiments on the real-time streaming protocol (RTSP) and simple mail transfer protocol (SMTP), which use Live555 and Exim implementations across multiple versions, demonstrate that this method yields more comprehensive protocol state machines with enhanced execution efficiency. Compared to the <i>L</i><Stack> _M ⁺ </Stack> algorithm implemented by AALpy, Act_Infer achieves an average reduction of approximately 40.7% in execution time and significantly reduces the number of connections and interactions by approximately 28.6% and 46.6%, respectively.</p>