Keyboards as a New Model of Computation

Authors Yoan Géran, Bastien Laboureix, Corto Mascle, Valentin D. Richard

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Author Details

Yoan Géran
  • ENS Paris-Saclay, France
Bastien Laboureix
  • ENS Paris-Saclay, France
Corto Mascle
  • ENS Paris-Saclay, France
Valentin D. Richard
  • ENS Paris-Saclay, France


We want to thank Pierre Béaur, Lucas Buéri, Jean-Baptiste Daval, Paul Gastin, Colin Geniet, Valentin Maestracci and Clément Théron for their helpful advice and feedback.

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Yoan Géran, Bastien Laboureix, Corto Mascle, and Valentin D. Richard. Keyboards as a New Model of Computation. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 49:1-49:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • formal languages
  • models of computation
  • automata theory


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