Inferring strings from suffix trees and links on a binary alphabet

A suffix tree, which provides us with a linear space full-text index of a given string, is a fundamental data structure for string processing and information retrieval. In this paper we consider the reverse engineering problem on suffix trees: given an unlabeled ordered rooted tree TT accompanied with a node-to-node transition function ff, infer a string whose suffix tree and its suffix links for inner nodes are isomorphic to TT and ff, respectively. Also, we consider the enumeration problem in which we enumerate all strings corresponding to an input tree and links. By introducing new characterizations of suffix trees, we show that the reverse engineering problem and the enumeration problem on suffix trees on a binary alphabet can be solved in optimal time.