Summary
The famous result of N. Friedman that any sorting algorithm uses at least O(n log n) relational operations in the worst case, even if the real number operations +,−,*, / can be used without any time account, is extended and generalized. Our main theorem can be used to calculate lower bounds for computations of functions if the operations <,+,−,*,/ are allowed and only the relational operators are counted. Friedman's sorting result and several other lower bounds are covered by the theorem. One of the results is of special interest for future directions of research, since it is possible to compute the max function of n arguments in a restricted domain with O(log n) relational operations.
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Schmitt, A. On the number of relational operators necessary to compute certain functions of real variables. Acta Informatica 19, 297–304 (1983). https://doi.org/10.1007/BF00265560
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DOI: https://doi.org/10.1007/BF00265560