Recognition of Topological Invariants by Modular Arrays

Abstract

In this paper we study recognition of topological invariant properties of patterns by use of finite, rectangular 2-dimensional, interactive arrays of finite state automata (hereafter called modular arrays). The use of modular arrays as pattern recognition devices has been studied by Atrubin [1] and by Unger [2]. Our aim is to show that modular arrays can not only recognize a large variety of topological invariants, but can do so in times that are almost minimal for a certain class of machines. We begin by describing our model of the modular array as a pattern recognition connectivity. Next, we introduce a fundamental transformation of patterns and prove several interesting properties of the transformation. Finally, we apply the transformation to modular arrays to obtain fast methods of recognizing a wide variety of topological invariants.