Imagine having a conversation with an AI that doesn't just respond when you're finished speaking, but actually listens, interrupts, and speaks concurrently, just like a human. That's the promise of full-duplex dialogue systems, and new research is bringing us closer to this conversational ideal. Traditionally, AI chatbots operate in half-duplex mode, meaning they wait for a complete input before generating a response. This creates a stilted, unnatural flow, far from the dynamic back-and-forth of human conversation. The challenge lies in enabling LLMs to process streaming input, understand context in real-time, and make autonomous decisions about when to speak, listen, or interrupt. This new research introduces a clever solution: a 'neural finite state machine' (neural FSM). This FSM allows the LLM to manage the flow of conversation by switching between 'SPEAK' and 'LISTEN' states. The LLM generates textual tokens for responses and emits control tokens to the neural FSM, deciding whether to respond, wait, or interrupt. This all happens in real-time, as the LLM processes a serialized view of the dialogue. The results are impressive. In simulated conversations, the full-duplex system reduced response latency by more than threefold compared to traditional half-duplex systems. In over half of the interactions, the system responded in under 500 milliseconds. Even more remarkably, a smaller LLM (8 billion parameters) achieved an 8% higher interruption precision rate than the best commercially available LLMs. This research opens doors to more natural and engaging human-AI interactions. Imagine voice assistants that can seamlessly handle interruptions, customer service bots that can anticipate your needs, or even AI companions that can truly participate in flowing conversations. While challenges remain, such as the reliance on separate speech recognition and generation modules, this work represents a significant step towards a future where talking to AI feels as natural as talking to another person.