The Lempel-Ziv Algorithm and Message Complexity.

We examine the first m words that the Lempel-Ziv algorithm parses from a binary message sequence and derive statistical properties of s sub m, the total number of digits these words contain. If m is not extremely large, the probability distribution of s sub m differs noticeably from the standard results about parsing in the limit of large m. However, even when m is small, s sub m retains enough of the limiting properties to remain an interesting indicator of message complexity.