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Real time recognition with cellular automata: A meaningful example. (English) Zbl 0776.68089

Let \(L\) be the language of all strings over the alphabet \(\{0,1\}\) such that the number of 1’s (in the string) equals the number of 1’s is the binary representation of the length (of the string). O. Ibarra, S. Kim, and S. Moran showed that \(L\) can be recognized (accepted) by a 1-dimensional cellular automaton (CA) in linear time, and they conjectured that it cannot be recognized by a CA in real time. This conjecture was disproved by the reviewer using a sequential machine model, the full scan Turing machine, which is equivalent to CA’s with respect to time complexity. The present paper gives an alternative, self-contained solution by a CA algorithm recognizing \(L\) in real time. This demonstrates the abilities of CA’s in signal processing and information management.

MSC:

68Q80 Cellular automata (computational aspects)
68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
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References:

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