Neural network for synthesizing deterministic finite automata

Deterministic finite automata are widely used in control systems: from abstract protocols such as TCP to mechanical devices such as elevators or traffic lights. Some of these systems are quite complex and can be defined only in terms of formal language theory. In this paper, we propose new approach for synthesizing finite automata from a dictionary of some language that uses neural networks. The results show that the proposed approach works correctly and quickly for automata with up to six states and four characters in the alphabet. For larger automata, the neural network suffers from the vanishing gradient problem, which is a big topic for further research.