Abstract
In this work, the two abstract automata GCM 0 and A -GCM 0 are introduced. A GCM 0 is a machine whose primitives are the basic euclidian operations with compass and ruler. It is shown that some elementary geometric problems can indeed be solved by a GCM 0-algorithm. On the other hand, our definition of GCM 0-constructible functions is so restrictive that not even the perpendicular projection of any arbitrary point tϵ E 2 onto the x-axis can be GCM 0-constructed. Therefore, the A -GCM 0 is introduced which has the additional capability to execute jumps under the condition that some x is in A . We shall give a generalclass of oracle sets A which yield a real extension of the class of constructible functions, and we shall consider another large class of oracles which do not. The last of our theorems deals with a uniform time bound of different constructions effected by nondeterministic GCM 0-operations.
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