Automata transformations of prefix decidable and decidable by Buchi superwords

Abstract

We show that the set of prefix decidable superwords is closed under finite automata and asynchronous automata transformations. We prove that structures of degrees of finite automata and asynchronous automata transformations contain an atom which consists of prefix decidable superwords with undecidable monadic theory (or undecidable by Buchi). Also we prove that the structure of degrees of asynchronous automata transformations contains an atom which consists of superwords with decidable monadic theory (decidable by Buchi).