Real-Time Recognition of Cyclic Strings by One-Way and Two-Way Cellular Automata

This paper discusses real-time language recognition by 1dimensional one-way cellular automata (OCAs) and two-way cellular automata (CAs), focusing on limitations of the parallel computation power. To clarify the limitations, we investigate real-time recognition of cyclic strings of the form uk with u ∈ {0, 1}+ and k ≥ 2. We show a version of pumping lemma for recognizing cyclic strings by OCAs, which can be used for proving that several languages are not recognizable by OCAs in real time. The paper also discusses the real-time language recognition of CAs by prefix and postfix computation, in which every prefix or postfix of an input string is also accepted, if the prefix or postfix is in the language. It is shown that there are languages L ⊆ Σ such that L is not recognizable by OCA in real-time and the reversal of L and the concatenation LΣ∗ are recognizable by CA in real-time. key words: cellular automata, OCA, parallel language recognition, pumping lemma, prefix recognition