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Castor quadruplorum

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Abstract

The busy beaver problem of Rado [6] is reexamined for the case of Turing machines given by quadruples rather than quintuples. Moreover several printing symbols are allowed. Some values of the corresponding beaver function are given and it is shown that this function for a fixed number of states and varying number of symbols is nonrecursive for three or more states and recursive for two states. As a byproduct we get that the minimal number of states in a universal Turing machine (quadruples) is three.

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Authors and Affiliations

  1. Abteilung Logik, Philosophisches Seminar, Christian-Albrechts-Universität, Olshausenstrasse 40, D-2300, Kiel, Federal Republic of Germany

    Arnold Oberschelp, Karsten Schmidt-Göttsch & Günter Todt

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  1. Arnold Oberschelp
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  2. Karsten Schmidt-Göttsch
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  3. Günter Todt
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Oberschelp, A., Schmidt-Göttsch, K. & Todt, G. Castor quadruplorum. Arch Math Logic 27, 35–44 (1988). https://doi.org/10.1007/BF01625831

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  • DOI: https://doi.org/10.1007/BF01625831

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