The field of automata theory and probabilistic modeling is witnessing significant developments, with a focus on integrating symbolic computation and deep learning. Researchers are exploring new architectures and algorithms that enable the exact simulation of probabilistic finite automata using neural networks, and the learning of symbolic Mealy automata with infinite input alphabets. Additionally, there is a growing interest in applying automata theory to probabilistic programming, with techniques such as weighted automata being used for exact inference in discrete probabilistic programs. Noteworthy papers in this area include:

• A paper that presents a formal and constructive theory for exactly simulating probabilistic finite automata using symbolic feedforward neural networks, and proves their learnability.
• A paper that proposes an active learning algorithm for symbolic Mealy automata, which supports infinite input alphabets and multiple output characters, and provides upper and lower bounds for the query complexity.