Generalized Factorizations of Words and Their Algorithmic Properties

We formalize the notion of a factorization of a word, a so-called F -factorization, introduced in [7] when solving some open problems on word equations. We show that most of the factorizations considered in the literature t well into that framework, and in particular that central algorithmic problems, such as the uniqueness or the synchronizability, remain polynomial time solvable for an important and large class of F -factorizations, namely for regular F -factorizations. TUCS Research Group Mathematical Structures in Computer Science 1Supported by Academy of Finland under grant 14047. Email:[email protected]. 2On leave from Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, 02{097 Warszawa, Poland. Email:[email protected]. 3Email: [email protected].