Title :
Two-dimensional formal languages and pattern recognition by cellular automata
Abstract :
A formal study of pattern recognition capabilities of cellular automata is undertaken based on a class of recently introduced grammars for two dimensions, the array grammars, which can be thought of as the two-dimensional generalization of context-sensitive grammars. The class of languages (patterns) generated by array grammars is shown to be precisely the class of languages accepted by cellular automata forming rook-connected finite subsets of the plane. Thus the usual generalization to rectangular array-bounded cellular automata is a special case of this class of machines. The concept of perimeter time is introduced as a natural measure of computing speeds for two-dimensional cellular spaces, and connectedness and convexity are related to this measure. The class of patterns with positive Euler number is shown to be linear-time recognizable by rectangular array-bounded cellular automata, thus solving an open problem of Beyer.
Keywords :
Automata; Extraterrestrial measurements; Formal languages; Nearest neighbor searches; Pattern recognition; Production; Retina; Time measurement; Two dimensional displays; Velocity measurement;
Conference_Titel :
Switching and Automata Theory, 1971., 12th Annual Symposium on
Conference_Location :
East Lansing, MI, USA
DOI :
10.1109/SWAT.1971.29