Comparison of complexity bounds for Bellman and Lupanov problems

Abstract

The report will focus on two issues. The first of these is to study the complexity of the calculation monomial in m variables. This problem was formulated in 1963 by R. Bellman and has an interesting history. The second problem, posed in 1988 by O.B. Lupanov, can be defined as the problem on the complexity of computing an element of an Abelian group. It is clear that the problems of Bellman and Lupanov are very similar and the results obtained for one of them, as a rule, are transferred to the other. However, in some cases, the complexity values for these tasks may differ significantly. Comparison of the complexity values for the Bellman and Lupanov problems will be discussed in the report.