Inaccessibility in decision procedures

To study physical the realizability of "computational" procedures, the notion of "inaccessibility" is introduced. As specific examples, the halting set of a universal Turing machine, the Mandelbrot set, and a riddled basin, all of which are defined by decision procedures, are studied. Decision procedures of a halting set of a universal Turing machine and the Mandelbrot set are shown to be inaccessible, that is, the precision of the decision in these procedures cannot be increased asymptotically as the error is decreased to 0. On the other hand, the decision procedure of a riddled basin is shown to have different characteristics regarding (in)accessibility, from the other two instances. The physical realizability of computation models is discussed in terms of the inaccessibility.