Constructing Factor Oracles

A factor oracle is a data structure for weak factor recognition. It is an automaton built on a string p of length m that is acyclic, recognizes at least all factors of p, has m+1 states which are all final, and has m to 2m−1 transitions. In this paper, we give two alternative algorithms for its construction and prove the constructed automata to be equivalent to the automata constructed by the algorithms in [1]. Although these new O(m2) algorithms are practically inefficient compared to the O(m) algorithm given in [1], they give more insight into factor oracles. Our first algorithm constructs a factor oracle based on the suffixes of p in a way that is more intuitive. Some of the crucial properties of factor oracles, which in [1] need several lemmas to be proven, are immediately obvious. Another important property however becomes less obvious. A second algorithm gives a clear insight in the relationship between the trie or dawg recognizing the factors of p and the factor oracle recognizing a superset thereof. We conjecture that an O(m) version of this trie-based algorithm exists.