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An internal factor of a word x is a word v such that x=uvw for some nonempty words u,w. The kernel of a set X of words is the set of words of X which are internal factors of words of X. Let φ be the syntactic morphism of the submonoid X* generated by X. We prove that if X is a code with empty kernel, the groups contained in the image by φ of the complement of the set of internal factors of the words...
We address the following issue: given a word w∈A* and a set of n nonempty words X, how does one determine efficiently whether w∈X* or not? We discuss several methods including an O(r×|w|+|X|) algorithm for this problem where r⩽n is the length of a longest suffix chain of X and |X| is the sum of the lengths of words in X. We also consider the more general problem of providing all the decompositions...
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