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With any word over the alphabet D = { r, r, u, ū }, we associate a connected picture in the following manner : the reading of each letter of this word induces a unit line : r ( r, u, ū resp.) stands for a right ( left, up, down resp.) move. We present a rewriting system which allows to obtain, from any word over D, all the words describing the same picture. Particularly, we give an algorithm to find...
A polyomino contour can be represented as a word over a four letter alphabet A. Each letter induces a unit line pointing one of the four directions (right, left, up and down). According to[b], checking whether a rational language R⊂A* contains a polyomino contour word is undecidable. We restrict the problem to convex polyominoes and we prove that, in this case, the problem turns out to be decidable.