An iterative array is a line of interconnected interacting finite automata. One distinguished automaton, the communication cell, is connected to the outside world and fetches the input serially symbol by symbol. Sometimes in the literature this model is referred to as cellular automaton with sequential input mode. We are investigating iterative arrays with a nondeterministic communication cell. All the other cells are deterministic ones. The number of nondeterministic state transitions is regarded as a limited resource which depends on the length of the input. It is shown that the limit can be reduced by a constant factor without affecting the language accepting capabilities, but for sublogarithmic limits there exists an infinite hierarchy of properly included real-time language families. Finally we prove several closure properties of these families.
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