Analysis of the Size of Antidictionary in DCA

Authors:
Julien Fayolle
Affiliations:
LRI/ Univ. Paris-Sud, CNRS, Orsay, France F-91405
Venue:
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Year:
2008

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Abstract

We analyze the lossless data compression scheme using antidictionary. Its principle is to build the dictionary of a set of words that do notoccur in the text (minimal forbidden words). We prove here that the number of words in the antidictionary, i.e., minimum forbidden words, behaves asymptotically linearly in the length of the text under a memoryless model on the generation of texts. The linearity constant is explicited. We use methods from analytic combinatorics.