Complete Variable-Length Codes: An Excursion into Word Edit Operations
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Given an alphabet A and a binary relation τ⊆ A * x A * , a language X ⊆ A * is τ-independent if τ (X) ∩ X = ∅; X is τ-closed if τ (X) ⊆ X. The language X is complete if any word over A is a factor of some concatenation of words in X. Given a family of languages F containing X, X is maximal in F if no other set of F can stricly contain X. A language X ⊆ A * is a variable-length code if any equation among the words of X is necessarily trivial. The study discusses the relationship between maximality and completeness in the case of τ-independent or τ-closed variable-length codes. We focus to the binary relations by which the images of words are computed by deleting, inserting, or substituting some characters.
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