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Comparing the Computational Complexity of Monomials and Elements of Finite Abelian Groups

Moscow University Mathematics Bulletin. 2022. Vol. 77. No. 3. P. 113–119.
Kochergin V.

Abstract: The computational complexity of the element (Formula presented.) of the Abelian group (Formula presented.) (it is supposed that kii for all i) and the computational complexity of the term (Formula presented.) are compared in the paper. The computational complexity means the minimal possible number of multiplication operations, and all the results of intermediate multiplications can be used multiple times. It is established that, if (Formula presented.), then the maximal possible difference and ratio of the above values asymptotically grow for (Formula presented.) as (Formula presented.) and (Formula presented.), respectively. © 2022, Pleiades Publishing, Inc.

Research target: Mathematics Computer Science
Language: English
DOI
Keywords: Computational ComplexityAddition chainsvectorial addition chainsfinite Abelian groupBellman’s problemKnuth’s problem
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