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Artificial automata replace, in part or in total, natural automata in systems, and properly disciplined models of natural automata become design models of artificial automata for replacement. In Part I, a summary of two sets of disciplines provided by a General Systems Theory is presented, and the importance of these disciplines to the modeling of three inherited abilities is indicated for a case study. A theorem is presented in the form of an algorithm to aid in the modeling of the ability to modify and extend knowledge structures. In Part II (appearing in the next issue), the proof of the theorem is given and the theorem is applied to the case study. Finally, the application of the disciplines of the General Systems Theory is indicated for a second casestudy of an industrial system of 10 interactive automata.

To program cellular automata is to define cell neighbourhood and cell‐state transition rules in order to design an automation which exhibits determined patterns in its evolution or which transforms a given image into another image. In general, a tool for the automatic programming of cellular automata should translate the tuple (source‐configuration) → (target‐configuration) into a set of cell‐state transition rules. This is a problem which has not been completely solved yet. Attempts to show examples of automatic programming of cellular automata using identification algorithms. Results obtained can be used in the design of massively parallel processors with cellular‐automata architecture and a conventional, as well as non‐traditional (e.g. molecular and chemical), elementary base.

Tolerance automata are defined and a decomposition theory for such entities is sought. It is shown that two major procedures of the classical algebraic theory produce difficulties in the tolerance case. A weaker approach, employing the idea of inertial tolerance, is presented. Finally, an explicit example is given which illustrates both the difficulties encountered and the theorems proved in the text.

Based on the concept of fuzzy sets of type 2 (or fuzzy‐fuzzy sets) defined by L. A. Zadeh, fuzzy‐fuzzy automata ate newly formulated and some properties of these automata are investigated. It is shown that fuzzy‐fuzzy languages characterized by fuzzy‐fuzzy automata are closed under the operations of union, intersection, concatenation, and Kleene closure in the sense of fuzzy sets of type 2, but are not closed under complement. The power of fuzzy‐fuzzy automata as an acceptor is the same as that of ordinary fuzzy automata and finite automata, though fuzzy‐fuzzy automata include fuzzy automata and finite automata as special cases. Finally, fuzzy‐fuzzy grammars are illustrated and it is shown that fuzzy‐fuzzy grammars with context‐free rules can generate context‐sensitive languages.

An interactive clothing system is one of the basic components of virtual reality. The clothing is implemented via design of two‐dimensional garment panels and putting the panels on an actor in a realistic way. We show how to ease this time consuming task by appealing to a hybrid cellular automaton as a parallel computing device. We draw our approach on a fact that the draping fabric bears a feature of natural parallelism. At a very short time scale behavior of any node point of a fabric depends only on the behavior of its closest neighboring node points. Therefore distant regions of the fabric can be simulated independently. Basing on the problem's natural parallelism we design two‐dimensional network of uniform locally connected hybrid automata that execute in parallel a particle model of draping behavior of clothes on a standing mannequin.

Select properties are presented for a graph model of a general automaton consisting of a processor, environment and time graph. The properties, stated in the form of theorems and corollaries, deal with connectedness, number of points and lines and indegree and outdegree as the model relates to the automaton's sets, functions and characteristics. The properties are illustrated by an example automaton.

Suitable ways of putting tolerance structures onto automata are sought. Inertial tolerance on the state set is discussed, but for black box automata an observed or even inertial tolerance on the output set is thought to be more appropriate. Tolerance inductions and coinductions are used to tolerate the remaining two sets in each case. A general definition of a tolerance automaton is suggested and the morphisms of the category defined. The particular case of an (M‐R) automaton is considered and required to yield a stable tolerance structure. Some illustrative examples are given.

Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space‐time configurations. No one has tried to analyze a generative power of cellular‐automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large‐scale spatially extended systems.

Let all but one cell be in alike state in initial configuration of a one‐dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three‐by‐three cell blocks occurred in the automaton's space‐time configuration.

The paper builds a hierarchy of generative diversity of one‐dimensional cellular automata with binary cell‐states and ternary neighborhoods, discusses necessary conditions for a cell‐state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions.

The method developed will be used – in conjunction with other complexity measures – to built a complete complexity maps of one‐ and two‐dimensional cellular automata, and to select and breed local transition functions with highest degree of generative morphological complexity.

The hierarchy built presents the first ever approach to formally characterize generative potential of cellular automata.

The theory of abstract neural automata has been proposed previously. Believes that in studying change of the structure of abstract neural automata, genetico‐variable structure must be considered. Abstract neural automata are considered to be cognizant machines, machines of thought. The basic effect on cognition and on the thought of heredity, such as genes is considered to be important in this discussion. Following the proof of the theorem of existence of abstract neural automata whose state space of single neuron (stochastic automaton) is Euclidean space E^d, the theorem of ergodicity of evolutionary process of genetico‐variable structure of abstract neural automata is proved.

A simple adaption of Dijkstra's algorithm for finding a minimum weight path on a weighted directed graph serves to solve the optimal control problem posed by Arbib for tolerance automata with cost function. Cumulative cost automata and the application of network theory to cost automata are also discussed.