A tight upper bound on the size of the antidictionary of a binary string

Abstract

A tight upper bound of the size of the antidictionary of a binary string is presented. And it is shown that the size of the antidictionary of a binary sting is always smaller than or equal to that of its dictionary. Moreover, an algorithm to reconstruct its dictionary from its antidictionary is given.

Keywords

• antidictionary
• minimum forbidden words
• suffix trees
• data compression
• ecg
• [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-cg] computer science [cs]/computational geometry [cs.cg]