Collage of two-dimensional words

Authors:
Christian Choffrut;Berke Durak
Affiliations:
Université Paris VII, Paris, France;Université Paris VII, Paris, France
Venue:
Theoretical Computer Science - The art of theory
Year:
2005

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Abstract

We consider a new operation on one-dimensional (resp. two-dimensional) word languages, obtained by piling up, one on top of the other, words of a given recognizable language (resp. two-dimensional recognizable language) on a previously empty one-dimensional (resp. two-dimensional) array. The resulting language is the set of words "seen from above": a position in the array is labeled by the topmost letter. We show that in the one-dimensional case, the language is always recognizable. This is no longer true in the two-dimensional case which is shown by a counter-example, and we investigate in which particular cases the result may still hold.