Statistical Properties of Factor Oracles

Factor and suffix oracles have been introduced in [1] in order to provide an economic and efficient solution for storing all the factors and suffixes respectively of a given text. Whereas good estimations exist for the size of the factor/suffix oracle in the worst case, no average-case analysis has been done until now. In this paper, we give an estimation of the average size for the factor/suffix oracle of an n-length text when the alphabet size is 2 and under a Bernoulli distribution model with parameter 1/2. To reach this goal, a new oracle is defined, which shares many of the properties of a factor/suffix oracle but is easier to study and provides an upper bound of the average size we are interested in. Our study introduces tools that could be further used in other average-case analysis on factor/suffix oracles, for instance when the alphabet size is arbitrary.