Characterizing the super-Turing computing power and efficiency of classical fuzzy Turing machines

The -rst attempts concerning formalization of the notion of fuzzy algorithms in terms of Turing machines are dated in late 1960s when this notion was introduced by Zadeh. Recently, it has been observed that corresponding so-called classical fuzzy Turing machines can solve undecidable problems. In this paper we will give exact recursion-theoretical characterization of the computational power of this kind of fuzzy Turing machines. Namely, we will show that fuzzy languages accepted by these machines with a computable t-norm correspond exactly to the union ∑0 1 ∪ ∏0 1 of recursively enumerable languages and their complements. Moreover, we will show that the class of polynomially time-bounded computations of such machines coincides with the union NP ∪ co-NP of complexity classes from the -rst level of the polynomial hierarchy. c © 2003 Elsevier B.V. All rights reserved.