J. Karhumaki and J. Manuch, Multiple factorizations of words and defect effect, TUCS Technical Report 329, (2000).  Home/Search   Document Details and Download   Summary   Related Articles

....defect effect. Graph Lemma (Theorem 4.1) is one such example. Under certain conditions (as in Example 7.3 below) it satisfies the above optimality requirement. In what follows we mention two other results on cumulative defect effect. Our first cumulative defect result is from Karhumaki and Manuch [18]. For this, recall that two factorizations s = u 1 u 0 u 1 = v 1 v 0 v 1 : of a biinfinite word s 2 A Z are disjoint, if the starting positions of u i and v j are different for all i; j 2 Z, see [22] or [18] for details. Theorem 6.1. Let X A be a prefix code. Let s 2 ....

.... Our first cumulative defect result is from Karhumaki and Manuch [18] For this, recall that two factorizations s = u 1 u 0 u 1 = v 1 v 0 v 1 : of a biinfinite word s 2 A Z are disjoint, if the starting positions of u i and v j are different for all i; j 2 Z, see [22] or [18] for details. Theorem 6.1. Let X A be a prefix code. Let s 2 A Z be a nonperiodic bi infinite word that has three disjoint factorizations over X . Then r c (X) card(X) 2. Theorem 6.1 gives rise to the following problem, 18] Problem 1. Let X A be a code. Let s 2 A Z be a ....

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J. Karhumaki and J. Manuch, Multiple factorizations of words and defect effect, TUCS Technical Report 329, (2000).

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