Abstract
This paper discusses real-time language recognition by 1-dimensional one-way cellular automata (OCA) and two-way cellular automata (CA), focusing on limitations of the parallel recognition power. We summarize the previous researches and investigate several languages to clarify the problems on real-time language recognition power of CA and OCA. It is shown that: 1. The language {ww : w ∈ {0,1}+} cannot be recognized by OCA in real time (this proposition is derived from a pumping lemma for cyclic strings); 2. L1There are languages L ⊂ Σ+ such that LΣ and its reversal can be recognized by CA in real time but L is not recognizable by OCA in real time; and 3. The language {w$w n : w ∈ {0,1}+, n ≥ 1}, as well as its reversal, is recognizable by CA in real time. The last result denies an Ibarra and Jiang’s conjecture [8].Key wordsCellular automataone-way cellular automataparallel language recognitionclosure under reversal
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