The influence of the data presentation on the computational power of machines
The influence of the data presentation on the computational complexity of functions is studied from a general point of view. The main emphasis lies on transformations Tυ induced by bijective changes ν of the presentation. Several sufficient conditions are given for very complex functions f such that Tυ−1 (f) is simple for an appropriate ν. On the other hand there are intrinsicially difficult functions that cannot be transformed into simple functions by any Tυ. Usually several functions shall be transformed simultaneously into simple functions. The following result gives a strong limitation of the power of data change: If Tυ is such that any primitive recursive (p.r.) f remains p.r., then no not p.r. function can be transformed into a p.r. function.
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