The publications are sources concerning the complexity of algorithms in respect of the complexity of input data are rather scarce, even though it is quite obvious that the complexity of algorithms strongly depends on the complexity of input data. At the same time expressions like 'almost all' or 'a certain part of' are commonly used in terminology concerning probabilistic algorithms and methods. In this paper we will attempt to take a closer look at what these expressions actually mean. Therefore we will aim to develop and systematize the theory of complexity functions.
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