By a method of heuristic search over the space of finite state automata with up to eight states, he was able to induce a recognizer for each of these languages (Tomita, 1982). Recognizers of finite-state languages have also been induced using first-order recurrent connectionistnetworks (Elman, 1990; Williams and Zipser, 1988; Cleeremans, Servan-Schreiber and McClelland, 1989). Generally speaking, these results were obtained by training the network to predict the next symbol (Cleeremans, Servan-Schreiber and McClelland, 1989; Williams and Zipser, 1988), rather than by training the network to accept or reject strings of different .lengths. Several training algorithms used an approximation to the gradient (Elman, 1990; Cleeremans, Servan-Schreiberand McClelland, 1989) by truncating the computation of the backward recurrence. The problem of inducing languages from examples has also been approached using second-order recurrent networks (Pollack, 1990; Giles et al., 1990). Using a truncated approximationto the gradient, and Tomita's training sets, Pollack reported that "none of the ideal languages were induced" (Pollack, 1990). On the other hand, a Tomita language has been induced using the complete gradient (Giles et al., 1991). This paper reports the induction of several Tomita languages and the extraction of the corresponding automata with certain differences in method from (Giles et al., 1991).

By a method of heuristic search over the space of finite state automata with up to eight states, he was able to induce a recognizer for each of these languages (Tomita, 1982). Recognizers of finite-state languages have also been induced using first-order recurrent connectionist networks (Elman, 1990; Williams and Zipser, 1988; Cleeremans, Servan-Schreiber and McClelland, 1989). Generally speaking, these results were obtained by training the network to predict the next symbol (Cleeremans, Servan-Schreiber and McClelland, 1989; Williams and Zipser, 1988), rather than by training the network to accept or reject strings of different.lengths. Several training algorithms used an approximation to the gradient (Elman, 1990; Cleeremans, Servan-Schreiber and McClelland, 1989) by truncating the computation of the backward recurrence. The problem of inducing languages from examples has also been approached using second-order recurrent networks (Pollack, 1990; Giles et al., 1990). Using a truncated approximation to the gradient, and Tomita's training sets, Pollack reported that "none of the ideal languages were induced" (Pollack, 1990). On the other hand, a Tomita language has been induced using the complete gradient (Giles et al., 1991). This paper reports the induction of several Tomita languages and the extraction of the corresponding automata with certain differences in method from (Giles et al., 1991).