For a Markovian source, we analyze the Lempel-Ziv parsing scheme that partitions sequences into phrases such that a new phrase is the shortest phrase not seen in the past. We consider three models: In the Markov Independent model, several sequences are generated independently by Markovian sources, and the ith phrase is the shortest preex of the ith sequence that was not seen before as a phrase ...

We the compare the number of phrases created by Ziv/Lempel '78 parsing of a binary sequence and of its reversal. We show that the two parsings can vary by a factor that grows at least as fast as the logarithm of the sequence length. We then show that under a suitable condition, the factor can even become polynomial, and argue that the condition may not be necessary.

Jing Tang Microsoft Corporation One Microsoft Way, 1/2061 Redmond, WA 98052 U.S.A. [email protected] For a Markovian source, we analyze the Lempel-Ziv parsing scheme that partitions sequences into phrases such that a new phrase is the shortest phrase not seen in the past. We consider three models: In the Markov Independent model, several sequences are generated independently by Markovian sou...

A word w is said to be closed if it has a proper factor x which occurs exactly twice in w, as prefix and suffix of w. Based on the concept Ziv–Lempel factorization, we define z-factorization finite infinite words. Then find m-bonacci words for all m≥2. We also classify prefixes