Factor Oracle: A New Structure for Pattern Matching

We introduce a new automaton on a word p, sequence of letters taken in an alphabet Σ, that we call factor oracle. This automaton is acyclic, recognizes at least the factors of p, has m +1 states and a linear number of transitions. We give an on-line construction to build it. We use this new structure in string matching algorithms that we conjecture optimal according to the experimental results. These algorithms are as efficient as the ones that already exist using less memory and being more easy to implement.