Combinatorial queries and updates on partial words

In this paper we define four combinatorial queries on partial words, asking if a factor of a partial word is a k-repetition, k-free, overlap-free, and primitive, respectively. We show how a given partial word can be preprocessed efficiently in order to answer each of these queries in constant time. Also, we define an update operation for partial words: add a new symbol at the rightmost end of a given partial word; further, we show that the data structures obtained during the preprocessing mentioned above can be updated efficiently in order to still be able to answer all the combinatorial queries, for the updated word, in constant time.