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:
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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);
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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
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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].
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Nakamura, K. (1999). Real-Time Language Recognition by One-Way and Two-Way Cellular Automata. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_20
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DOI: https://doi.org/10.1007/3-540-48340-3_20
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