Based On Fuzzy Neural Network Automata

Grammatical inference is a suitable technique for solving the problems such as speech recognition, object recognition in images, protein structure prediction, gene structure prediction, etc. To carry out the grammatical inference, using artificial neural networks is an appropriate approach. Since the equivalence between grammars and automata, grammatical inference using neural networks, in essence, is extracting automata from neural networks.In this thesis, we introduce the neural network approach for grammatical inference, which will be illustrated in two perspectives: the traditional grammatical inference and fuzzy grammatical inference, and we mainly concern about the topologies of the neural networks, their learning algorithms and the rule extraction algorithms. On the base of summarizing former researchers' work, we propose a new neural network architecture for fuzzy grammatical inference by introducing discretization into the second-order recurrent neural network, and provide the network with the learning algorithm.Besides, we introduce the minimization algorithm of automata. First, we summarize the work done on fuzzy automata. Then, we propose the definition of refining equivalence and refining congruence, and apply it to lattice automata. By using the theory of algebra, we derive a new minimization algorithm for lattice automata.More specifically, the main results are shown below:1. Work on fuzzy automata based on neural networks. First, we introduce discretization into the network topology, propose the multi-level discretization function, and construct a self-clustering recurrent neural network, which is supportive of multiple input symbols and is capable for fuzzy grammatical inference. We also provide the pseudo-gradient learning algorithm for the proposed neural network. Once the network has been successfully trained, the internal states are finite and stable, thus solving the problem of stability of the inner states of the trained network when it is fed with sufficiently long and unseen strings, and save the clustering process to extract automaton from the network, hence simplify the process of learning and extraction of fuzzy automaton. After proposing the network architecture and learning algorithm, we give the results of simulation.2. Work on the minimization algorithm of lattice automata. First, we put forward the definitions of refining equivalence and refining congruence, and apply it to the state space of a lattice automaton, using the algebraic theory, we get the equivalence class and quotient space, thus form the quotient lattice automaton. Then, based on the definition of equivalence between two lattice automata, we prove the equivalence between the lattice automaton and its quotient automaton, while based on the definition of the minimal property of a lattice automaton, we show that the quotient automaton has the minimal property. After the proof, we propose the minimization algorithm of lattice automata which is applicable on computers, and give an example to illustrate it.We use the methods such as comparison, induction, analysis, synthesis, etc for logical proof, and we do experiments to simulate and give examples to verify the feasibility of our algorithm.