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We propose an approach that connects recurrent networks with different ordersof hidden interaction with regular grammars of different levels of complexity.We argue that the correspondence between recurrent networks and formalcomputational models gives understanding to the analysis of the complicatedbehaviors of recurrent networks. We introduce an entropy value that categorizesall regular grammars into three classes with different levels of complexity,and show that several existing recurrent networks match grammars from eitherall or partial classes. As such, the differences between regular grammarsreveal the different properties of these models. We also provide a unificationof all investigated recurrent networks. Our evaluation shows that the unifiedrecurrent network has improved performance in learning grammars, anddemonstrates comparable performance on a real-world dataset with morecomplicated models.

Connecting First and Second Order Recurrent Networks with Deterministic Finite Automata