Limited Two-Way Deterministic Finite Automata with Advice

External assistance in the form of strings called advice is given to an automaton in order to make it a non-uniform model of computation. Automata with advice are then examined to better understand the limitations imposed by uniformity, which is a typical property shared by all feasible computational models. The main contribution of this paper is to introduce and investigate an extension of the model introduced by Küçük et al. [6]. The model is called circular deterministic finite automaton with advice tape (cdfat). In this model the input head is allowed to pass over input multiple times. The number of allowed passes over the input, which is typically a function of input length, is considered as a resource besides the advice amount. The results proved for the model include a hierarchy for cdfat with real-time heads, simulation of 1w/1w cdfat by 1w/rt cdfat, lower bounds of resources provided to a cdfat in order to make it powerful enough to recognize any language, utilizable advice limit regardless of the allowed pass limit, a relation between utilizable pass limit and advice limit, and some closure properties.