Classical Computability and Fuzzy Turing Machines

BENJAMÍN RENÉ CALLEJAS BEDREGAL; SANTIAGO FIGUEIRA

LECTURE NOTES IN COMPUTER SCIENCE

Springer-Verlag

Año: 2006 vol. 3887 p. 154 - 165

0302-9743

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 [Wiedermann, J. Characterizing the super-Turing computing power and efficiency of classical fuzzy Turing machines. Theoretical Computer Science. 317 (2004) 61--69] 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.