Equivalence in knowledge representation: Automata, recurrent neural networks, and dynamical fuzzy systems

Neurofuzzy systems-the combination of artificial neural networks with fuzzy logic-have become useful in many application domains. However, conventiona l neurofuzzy models usually need enhanced representational power for applic ations that require context and sate (e.g., speech, rime series prediction, control). Some of these applications can be readily modeled as finite stat e automata. Previously, it was proved that deterministic Smite state automa ta (DFA) can be synthesized by or mapped into recurrent neural networks by directly programming the DFA structure into the weights of the neural netwo rk. Based on those results, a synthesis met,Bod is proposed for mapping fuz zy finite state automata (FFA) into recurrent neural networks. Furthermore, this mapping is suitable for direct implementation in very large scale int egration (VLSI), i.e., the encoding of FFA as a generalization of the encod ing of DFA in VLSI systems. The synthesis method requires FFA to undergo a transformation prior to being mapped into recurrent networks. The neurons a re provided with an enriched functionality in order to accommodate a fuzzy representation of FFA stares. This enriched new on functionality also permi ts fuzzy parameters of FFA to be directly represented as parameters of the neural network. We also prove the stability of fuzzy Smite state dynamics o f the constructed neural networks for finite values of network weight and, through simulations, give empirical validation of the proofs. Hence, we pro ve various knowledge equivalence representations between neural and fuzzy s ystems and models of automata.