Keyboards as a New Model of Computation

We introduce a new formalisation of language computation, called keyboards. We consider a set of atomic operations (writing a letter, erasing a letter, going to the right or to the left) and we define a keyboard as a set of finite sequences of such operations, called keys. The generated language is the set of words obtained by applying some non-empty sequence of those keys. Unlike classical models of computation, every key can be applied anytime. We define various classes of languages based on different sets of atomic operations, and compare their expressive powers. We also compare them to rational, context-free and context-sensitive languages. We obtain a strict hierarchy of classes, whose expressiveness is orthogonal to the one of the aforementioned classical models. We also study closure properties of those classes, as well as fundamental complexity problems on keyboards. 2012 ACM Subject Classification Theory of computation