This paper deals with a wire-routing algorithm for a building-block LSI. This algorithm has several features which sharply define it from previous techniques. The most noteworthy one among them is that it can achieve perfect wirability. This feature enables a design automation of an LSI layout pattern without any human supports.

If an object to be observed is much larger than the field of vision, we should observe it part by part as in the case of eye fundus photographs or gastrocamera photographs. Subpictures obtained through partial observation should be assembled into a mosaic picture which shows the whole object. An arrangement graph which shows adjacency and spatial differences among subpictures is defined, and the properties of the arrangement graph are discussed. Furthermore, the condition of the arrangement graph for a mosaic picture to be defect-free, that for a subpicture to be redundant in a mosaic picture, and the way to find subpictures surrounding defect areas of a mosaic picture are shown. The discussion is based on a graph theory and a notion of space vectors.

An on-off sequence of an unknown signal pattern that is time-varying or fixed is dealt with. The optimum analogue feedback signal is obtained, which minimizes the average energy transmitted in the forward direction. The nonsupervised situation is also discussed. The effectiveness of the feedback method over the nonfeedback method is twice for the typical case.

A learning model of fuzzy formal language is proposed and discussed. We continue training the learning machine by giving sets of sentences sequentially. As a result of parsing of the given teaching sentences, the learning machine reinforces fuzzy grades of membership of productions in an inherent fuzzy grammar of the machine. The convergence of the proposed model is considered, and it is shown that the grades of membership of desired productions are intensified by choosing an adequate teaching sequence of the sentence set. Furthermore, a concept of ``strongly equivalent,'' in which two grammars are not distinguished by any teaching sequence, is introduced.

The orthogonal expansion of many-valued logical functions is described and some approximate forms derived from it are discussed. A method of logical design of many-valued functions, especially threshold functions, using a single-threshold element is proposed based on the approximate forms.

Methods of synchronization for an unknown signal sequence by learning procedure, which computes a posteriori probabilities for the signal location, are presented. First, to avoid the difficulties of the interference between successive intervals, a signal sequence with ample guard spaces for getting rid of the interference is treated. Next, the case without guard space is treated. To the nonsupervised case, some methods are applied. The methods proposed in this paper have a form of double learning with respect to the unknown signal form and the signal location. Also some results of computer simulation are presented.

Some recognizers for stochastic time-varying patterns with additive noise are studied. As in binary communication channels with fading, it is supposed that the fluctuation of a pattern (or signal) may be approximated by a stationary Gaussian autoregressive process with known parameters. Each measurement belongs to either of two classes: the pattern plus noise or noise alone. Under these assumptions, optimum dichotomizers with supervized learning are discussed. To the nonsupervised problems, the decision-directed approach and the modified-decision-directed approach are applied. Also some experimental results are presented.

A method of classifying patterns using fuzzy relations is described. To start with, we give a suitable value of the measure of subjective similarity to each pair of patterns that is taken from the population of patterns to be classified. Then a similitude between any two patterns is calculated by using the composition of a fuzzy relation. The similitude induces an equivalence relation. Consequently, we can classify the present population of the patterns into some classes by the equivalence relation. An experiment of the classification of portraits has been performed to test the method proposed here.