Detecting leftmost maximal periodicities

Periodicities are nonempty strings of the form pmq with m 12 and q a prefix of p. The integer m is called the power of the periodicity, “he length of p (written lpi) is the period length, and the periodicity length is the total length of pmq. This note presents a new algorithm to output a list of occurrences of periodicities within a string. The list does not contain all periodicities within the given string, but it is guaranteed to contain any periodicity which is leftmost and maximal. Informally, a substring of a string is a maximal periodicity provided that it is a periodicity such that neither the character which precedes nor the character which follows the substring can be added without destroying the periodicity. A substring of a string is leftmost provided that there is no previous occurrence of the substring within the given string. For a given string, the list of periodicities produced by the algorihm provides immediate answers to problems such as:

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