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Classical Computability and Fuzzy Turing Machines

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LATIN 2006: Theoretical Informatics (LATIN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3887))

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Abstract

We work with fuzzy Turing machines (ftms) and we study the relationship between this computational model and classical recursion concepts such as computable functions, r.e. sets and universality. ftms are first regarded as acceptors. It has recently been shown in [23] that these machines have more computational power than classical Turing machines. Still, the context in which this formulation is valid has an unnatural implicit assumption. We settle necessary and sufficient conditions for a language to be r.e., by embedding it in a fuzzy language recognized by a ftm and we do the same thing for difference r.e. sets, a class of “harder” sets in terms of computability. It is also shown that there is no universal ftm. We also argue for a definition of computable fuzzy function, when ftms are understood as transducers. It is shown that, in this case, our notion of computable fuzzy function coincides with the classical one.

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Author information

Authors and Affiliations

  1. Department of Informatics and Applied Mathematics, Laboratory of Logic and Computational Intelligence, Federal University of Rio Grande do Norte, Natal, RN, Brazil

    Benjamín René Callejas Bedregal

  2. Department of Computer Science, FCEyN, University of Buenos Aires, Buenos Aires, Argentina

    Santiago Figueira

Authors
  1. Benjamín René Callejas Bedregal
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  2. Santiago Figueira
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Editor information

Editors and Affiliations

  1. School of Business, Universidad Adolfo Ibáñez, Chile

    José R. Correa

  2. Dept. of Computer Science, University of Chile, Blanco Encalada 2120, 3er piso, Santiago, Chile

    Alejandro Hevia

  3. Dept. Ing. Matemática & Ctr. de Modelamiento Matemático, UMI 2807 U. Chile–CNRS, Chile

    Marcos Kiwi

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© 2006 Springer-Verlag Berlin Heidelberg

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Bedregal, B.R.C., Figueira, S. (2006). Classical Computability and Fuzzy Turing Machines. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_18

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  • DOI: https://doi.org/10.1007/11682462_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32755-4

  • Online ISBN: 978-3-540-32756-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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