Structural properties, local and asymptotic, of members of a class of simple, realtime generable sequences are analyzed.

Uniform tag sequences

A general decomposition scheme is described which allows the realization of a given synchronous sequential machine as an interconnection of identical two-state modules. The bound on the fan-in and fan-out of each module is independent of the number of states in the given machine.

Bounded fan-in, bounded fan-out uniform decompositions of synchronous sequential machines

A brief list of the applications of topology to various disciplines is given in the introduction (dynamical systems, automata theory, psychology, linguistics, biology, economics) It is argued that topology plays an important role in general systems theory as well. This has already been shown by Cornacchio and Hammer. Unfortunately, the topologies needed for this purpose have to be generalized topologies in which Kuratowski closure axioms do not hold Work involving generalized topologies is usually associated with Hammer who published numerous papers on this topic. There have been some earlier isolated attempts to develop some generalizations, e.g. by Moore, Tarski, Birkhoff, Ore, but the matter has not been treated systematically. It is virtually unknown that there exists a very systematic treatment of the topic of generalized topologies in a series of papers which originated from the topological seminar conducted by Eduard c ech in Brno, Czechoslovakia, in the years 1936-1939 The purpose of this article ...

GENERALIZED TOPOLOGIES AND THEIR RELEVANCE TO GENERAL SYSTEM† Bibliography of Works of the č ech Topological School

The authors review a 15-year research effort to develop a method for the design of finite-state controls for continuous-state processes. The method solves a particular discrete-event control problem using techniques of automata theory. Design algorithm development for linear single-input single-output plants during 1980-5 is examined. Open research issues are described. >

Finite state control of continuous-state process: progress and prospects

A universal logic module of n variables (ULM-n) can be considered as a 2n-in-1 multiplexer (inverse binary tree) whose code is determined by the presentation of external variables. This interpretation permits synthesis of sequential machines. Starting from the state transition map, any sequential machine can be realized by delayed ULM's and OR gates. The decomposition concept of Weiner and Hopcroft is generalized to form a uniform synthesis of n-variable sequential machines.

Delayed Universal Logic Modules and Sequential Machine Synthesis

In this paper we study some relations between the continuity of sequence transformations and their realizability by logic nets. The main results discussed include: the Curtis-Hedlund-Lyndon theorem which states that, if a sequence transformation is continuous and unitary (commutative with the shift transformation), then it can be realized by a net without feedback, and, the extension of this theorem to the finitary case. We find that unitary transformations are realized by definite automata, and finitary transformations are realized by indefinite automata. The term ``automata'' is used here in a modification of its usual sense, and we explore the relation between the conventional and modified notions. Many of the concepts and more significant mathematical results in this report can be found in another context in works by Hedlund and others. What may be new and of interest to computer scientists, we believe, is their application to the theory of sequential circuits.

Continuity and Realizability of Sequence Transformations

In recent years adaptive threshold ele-ments have been used as the basis for learning machines such as the Perceptron [1] and Adaline [2]. To the author's knowledge there has been no previously reported work on a systematic study of algorithms, used in learning machines, to modify the weightvalues of threshold elements.

S. Winograd

Papers

Continuity and Realizability of Sequence Transformations

On the Number of Transitions Entering the States of a Finite Automaton