Abstract
Wyner and Ziv (IEEE Trans. vol.IT-35, p.1250-8 of 1989) have proved that the typical length of a repeated subword found within the first n positions of a stationary sequence is (1/h) log n in probability where h is the entropy of the alphabet. They used this finding to obtain insights into certain universal data compression schemes, most notably the Lempel-Ziv algorithm. They have also conjectured that their result can be extended to a stronger almost sure convergence. This paper settles this conjecture in the negative. It proves, under some additional assumption regarding mixing conditions, that the length of a repeated subword oscillates with probability one between (1/h/sub 1/) log n and (1/h/sub 2/) log n where h/sub 2/ >
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