Special factors and the combinatorics of suffix and factor automata

Abstract

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 S A and L F A of words having respectively suffix automaton and factor automaton with the minimal possible number of states.