A recent watermarking scheme for language models achieves distortion-free embedding and robustness to edit-distance attacks. However, it suffers from limited generation diversity and high detection overhead. In parallel, recent research has focused on undetectability, a property ensuring that watermarks remain difficult for adversaries to detect and spoof. In this work, we introduce a new class of watermarking schemes constructed through probabilistic automata. We present two instantiations: (i) a practical scheme with exponential generation diversity and computational efficiency, and (ii) a theoretical construction with formal undetectability guarantees under cryptographic assumptions. Extensive experiments on LLaMA-3B and Mistral-7B validate the superior performance of our scheme in terms of robustness and efficiency.