Real-Time Language Recognition by One-Dimensional Cellular Automata

Pattern recognition by parallel devices is investigated by studying the formal language recognition capabilities of one-dimensional cellular automata. The precise relationships of cellular automata to iterative automata and to Turing machines are established: In both cases, cellular automata are inherently faster. The relationship of context-free languages to the languages recognized in real time by bounded cellular automata is detailed. In particular, nondeterministic bounded cellular automata can recognize the context-free languages in real time. The deterministic case remains open, but many partial results are derived. Finally, closure properties and cellular automata transformation lemmas are presented.