Gaining Power by Input Operations: Finite Automata and Beyond

We summarize results on extended finite automata, which are basically finite state machines with the additional ability to manipulate the still unread part of the input. Well-known manipulation functions are reversal, left-revolving, right-revolving, and circular interchanging, or even biologically motivated functions as hairpin inversion. We mainly focus on the computational power of these machines and on the closure properties by standard formal language operations of the induced language families. Moreover, we also discuss several generalizations of this concept, the natural generalization to hybrid extended finite automata, which allows several input manipulation functions, and in particular, extended pushdown automata, which lead to an alternative characterization of Khabbaz hierarchy of languages. We do riot prove these results but we merely draw attention to the big picture, some of the main ideas involved, and open problems for further research.