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# Accession Number:

## AD0699502

# Title:

## RECOGNITION OF TOPOLOGICAL INVARIANTS BY ITERATIVE ARRAYS.

# Descriptive Note:

## Doctoral thesis,

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE PROJECT MAC

# Report Date:

## 1969-10-24

# Pagination or Media Count:

##
145.0

# Abstract:

## A study is made of the recognition and transformation of figures by iterative arrays of finite state automata. A figure is a finite rectangular two-dimensional array of symbols. The iterative arrays considered are also finite, rectangular, and two-dimensional. The automata comprising any given array are called cells and are assumed to be isomorphic and to operate synchronously with the state of a cell at time t 1 being a function of the states of it and its four nearest neighbors at time t. At time t 0 each cell is placed in one of a fixed number of initial states. The pattern of initial states thus introduced represents the figure to be processed. The resulting sequence of array states represents a computation based on the input figure. If one waits for a specially designated cell to indicate acceptance or rejection of the figure, the array is said to be working on a recognition problem. If one waits for the arrays to come to a stable configuration representing an output figure, the array is said to be working on a transformation problem. In addition to the formal results, several open questions are presented and some iterative programming techniques are considered. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#