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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, recursively enumerable (r.e.) sets and universality. FTMs are first regarded as acceptors. It has recently been shown by J. Wiedermann 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. We do the same thing for n-r.e. set. It is shown that there is no universal fuzzy machine, and "universality" is analyzed for smaller classes of FTMs. We 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. © 2007 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:On the computing power of fuzzy Turing machines
Autor:Bedregal, B.C.; Figueira, S.
Filiación:Departamento de Informática e Matemática Aplicada, Laboratório de Lógica e Inteligência Computacional, Universidade Federal do Rio Grande do Norte, Campus Universitário s/n, Lagoa Nova, Natal-RN, CEP 59.072-970, Brazil
Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria, C1428EGA Buenos Aires, Argentina
Palabras clave:Fuzzy function; Fuzzy set; Fuzzy Turing machine; Recursively enumerable set; Universal machine; Computational efficiency; Computer programming languages; Recursive functions; Transducers; Turing machines; Fuzzy functions; Fuzzy Turing machine; Recursively enumerable sets; Universal machines; Fuzzy sets
Año:2008
Volumen:159
Número:9
Página de inicio:1072
Página de fin:1083
DOI: http://dx.doi.org/10.1016/j.fss.2007.10.013
Título revista:Fuzzy Sets and Systems
Título revista abreviado:Fuzzy Sets Syst
ISSN:01650114
CODEN:FSSYD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01650114_v159_n9_p1072_Bedregal

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Citas:

---------- APA ----------
Bedregal, B.C. & Figueira, S. (2008) . On the computing power of fuzzy Turing machines. Fuzzy Sets and Systems, 159(9), 1072-1083.
http://dx.doi.org/10.1016/j.fss.2007.10.013
---------- CHICAGO ----------
Bedregal, B.C., Figueira, S. "On the computing power of fuzzy Turing machines" . Fuzzy Sets and Systems 159, no. 9 (2008) : 1072-1083.
http://dx.doi.org/10.1016/j.fss.2007.10.013
---------- MLA ----------
Bedregal, B.C., Figueira, S. "On the computing power of fuzzy Turing machines" . Fuzzy Sets and Systems, vol. 159, no. 9, 2008, pp. 1072-1083.
http://dx.doi.org/10.1016/j.fss.2007.10.013
---------- VANCOUVER ----------
Bedregal, B.C., Figueira, S. On the computing power of fuzzy Turing machines. Fuzzy Sets Syst. 2008;159(9):1072-1083.
http://dx.doi.org/10.1016/j.fss.2007.10.013