The Busy Beaver Competition: a historical survey Pascal Michel To cite this version: Pascal Michel. The Busy Beaver Competition: a historical survey. 2017. hal-00396880v6 HAL Id: hal-00396880 https://hal.archives-ouvertes.fr/hal-00396880v6 Preprint submitted on 4 Sep 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Busy Beaver Competition: a historical survey Pascal MICHEL∗ Equipe´ de Logique Math´ematique, Institut de Math´ematiques de Jussieu–Paris Rive Gauche, UMR 7586, Bˆatiment Sophie Germain, case 7012, 75205 Paris Cedex 13, France and Universit´ede Cergy-Pontoise, ESPE, F-95000 Cergy-Pontoise, France
[email protected] Version 6 September 4, 2019 Abstract Tibor Rado defined the Busy Beaver Competition in 1962. He used Turing machines to give explicit definitions for some functions that are not computable and grow faster than any computable function. He put forward the problem of computing the values of these functions on numbers 1, 2, 3, . .. More and more powerful computers have made possible the computation of lower bounds for these values. In 1988, Brady extended the definitions to functions on two variables. We give a historical survey of these works.