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Abstract
In [13], different regulation mechanisms imposed upon /c-limited TOL systems have been considered. Additionally, in this paper we investigate regularly controlled /c-limited TOL systems with or without random context and with or without appearance checking. By these kinds of control mechanisms, we further increase the generative power of the systems. Especially, we can demonstrate that for every k e IN, the family of random context regularly controlled /clTOL languages with appearance checking equals the family of recursively enumerable languages.