Abstract
We consider various generalizations of the effective exponentiation problem, also known as the addition chains problem in additive terminology. We attempt to evaluate and consistently compare the results and the methods that were used to obtain them. The considered generalizations are complexity problems (i.e. finding the minimum number of required operations) for the computation a monomial of many variables, a set of powers, elements of finite Abelian groups, elements of free semigroups, systems of monomials, systems of integer linear forms, systems of elements of free Abelian groups along with some other problems. For all these directions of research we overview both the classical results and the results of the author and his followers.
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