Quantity Analysis on the Chaining of Repetition Free Words Considering the VDE Composition Rule

The motivation behind this contribution was raised during the examination of the boundary value patterns of the Virtual Dictionary Extension (VDE) compression method, which is a re-weighted extension of the lossless, universal compression method, LZW. During the VDE compression method words are stored in the so called compression dictionary, therefore the base unit of the boundary value pattern is the word. The application of VDE is reasonable over patterns where the relatively long base fragments are recurring with short deviance at the end. In our earlier work we found and proved the existence of the pattern which results the best compression ratio. However, determination of the input pattern, which results the worst compression ratio (or worst case), is much more complicated, since it depends on the recursive extension of words.