On the Additive Complexity of Some Integer Sequences

The paper presents several results concerning the complexity of calculations in the model of vector addition chains. A refinement of N. Pippenger’s upper bound is obtained for the complexity of the class of integer matrices with the constraint on the size of the coefficients as up to . Next, we esta...

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Bibliographic Details
Published inMathematical Notes Vol. 115; no. 3-4; pp. 378 - 389
Main Author Sergeev, I. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.04.2024
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Complexity
Integers
Mathematics
Mathematics and Statistics
Polynomials
Sequences
Upper bounds
set
sumset
sum-free set
cycle graph
addition chain
complexity lower bound
Sidon set
rectifier circuit
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Summary:The paper presents several results concerning the complexity of calculations in the model of vector addition chains. A refinement of N. Pippenger’s upper bound is obtained for the complexity of the class of integer matrices with the constraint on the size of the coefficients as up to . Next, we establish an asymptotically tight bound on the complexity of сomputation of the number in the base of powers of . Based on generalized Sidon sequences, constructive examples of integer sets of cardinality are constructed: sets, with polynomial size of elements, having the complexity for any and sets, with the size of the elements, having the complexity .
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434624030106