Special factors and the combinatorics of suffix and factor automata

The suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata. We also characterize the languages L_SA and L_FA of words having respectively suffix automaton and factor automaton with the minimal possible number of states.