Abstract
Pictures of functions of one variable in the natural number theory are introduced as patterns over {0,1} in the first quadrant. It is proved that the set of pictures of all computable functions of one variable is obtained as the bottom planes of three-dimensional arrays accepted by some nondeterministic automaton on ω3-tapes. To our surprise, it is also shown that a set of pictures of functions containing a noncomputable function is deterministically obtained in a similar way. Further, it is proved that the set of initial segments of pictures of all computable functions and/or the noncomputable function is accepted by a deterministic Turing rectangular array acceptor.
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