Abstract
To obtain a definition of an algorithm using oracle A it is necessary to modify Kolmogorov’s formulation from chap. 1.1 as follows. An oracle A is a subset of an aggregate. An oracle-algorithm has a “questioning device” which is an auxiliary algorithm ℑ defined (i.e. giving a result) on all possible states S. Each step in the process determined by an oracle-algorithm depends not only on the current state S but also on the truth value of the statement ℑ(S) ∈ A. Thus the operator of the immediate transformation ΩΓ (producing the next state S*) is now a function of two arguments — of a state S and of the number b equal to 0 or 1 depending on the truth value of the statement ℑ(S) ∈ A. An oracle algorihm with an oracle A is also called an algorithm relative to A (see [Rog 67, sect.9.2]).
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© 1993 Springer Science+Business Media Dordrecht
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Uspensky, V., Semenov, A. (1993). The concept of a relative algorithm, or an oracle algorithm. In: Algorithms: Main Ideas and Applications. Mathematics and Its Applications, vol 251. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8232-2_15
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DOI: https://doi.org/10.1007/978-94-015-8232-2_15
Publisher Name: Springer, Dordrecht
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