We define fuzzy neuroidal nets in a way that enables to relate their
computations to computations of fuzzy Turing machines. Namely, we show that the polynomially space-bounded computations of fuzzy Turing machines with a polynomial advice function are equivalent to the computations of a polynomially-sized family of fuzzy neuroidal nets. The same holds for fuzzy neural nets which are a special case of fuzzy neuroidal nets. This result ranks discrete fuzzy neural nets among the most powerful computational devices known in the computational complexity theory.
It is shown that tlie computational power of iion-uniform infinite families of (discrete) neural nets reading their inputs sequentially (so-called neuromata), of polynomial size, equals to PSPACE/poly, and of logarithmic size to LOGSPACE/loy. Thus, such farnilies posses super-Turiug computational power. From computational complexity point of view the above mentioned results rank the respective families of neuromata among the most powerful computational devices known today.