Abstract
We are interested in the concept of locally complete set: A subset X of the free monoid is locally complete if a code Y⊂A ∗ exists, with Y≠A, X ∗⊂Y ∗ , and such that both the sets X ∗ and Y ∗ have the same sets of factors. Our contribution is based on the three following results: • A characterization of local completeness for very thin sets in terms of morphic images. • A polynomial time algorithm for deciding whether a finite code is locally complete. • A polynomial time algorithm for deciding whether a finite maximal code is decomposable.
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