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Parallel language recognition in constant time by cellular automata

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Summary

It is proved that the set of all languages accepted within a fixed, language dependent number of steps by deterministic one dimensional cellular acceptors is a proper subset of the set of all regular languages.

A combinatorial condition is stated which is necessary and sufficient for a language to be recognizable in constant time by a deterministic one dimensional cellular automaton.

It is shown that the question of whether or not the language generated by a given context-sensitive grammar is recognizable in constant time is algorithmically unsolvable. The question becomes solvable if a regular grammar is given.

Finally it is proved that the set of all languages that can be accepted by non-deterministic one dimensional cellular acceptors is equal to the set of all regular languages.

In conclusion some generalizations to n-dimensional languages and array languages are mentioned.

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Authors and Affiliations

  1. Technische Hogeschool Delft, Onderafdeling der Wiskunde, Julianalaan 136, NL-2628, BL Delft, The Netherlands

    R. Sommerhalder & S. C. van Westrhenen

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  1. R. Sommerhalder
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  2. S. C. van Westrhenen
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Sommerhalder, R., van Westrhenen, S.C. Parallel language recognition in constant time by cellular automata. Acta Informatica 19, 397–407 (1983). https://doi.org/10.1007/BF00290736

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