A study of some addition chain problems

In this paper, some mathematical properties of the shortest-length addition chain are found for certain integers whose binary patterns meet some special forms; and the correctness of these properties is proved.

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Published in:International journal of computer mathematics Vol. 22; no. 2; pp. 117 - 134
Main Authors: Tsai, Y.H., Chin, Y.H.
Format: Journal Article
Language:English
Published: Gordon and Breach Science Publishers 01.01.1987
Subjects:
Addition Chain
big step
double step
F.1.3 [Complexity Classes]-relations among complexity measures
F.2.1 [Numer-ical Algorithms and Problem Complexity]-number-theoretic computations
F.l.l [Computation by Abstract Devices]
G.l [Numerical Analysis]-Computer Arithmetic
long-five
Models of Computation-computability theory
short-five
small step
special four
the shortest-length addition chain
ISSN:0020-7160, 1029-0265
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Abstract In this paper, some mathematical properties of the shortest-length addition chain are found for certain integers whose binary patterns meet some special forms; and the correctness of these properties is proved.
AbstractList In this paper, some mathematical properties of the shortest-length addition chain are found for certain integers whose binary patterns meet some special forms; and the correctness of these properties is proved.
Author Chin, Y.H.
Tsai, Y.H.
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  organization: Institute of Computer and Decision Sciences , National Tsing-Hua University
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Cites_doi 10.1090/S0002-9904-1939-07068-7
10.1137/0210047
10.1215/S0012-7094-62-02948-4
10.1090/S0002-9939-1953-0054618-X
10.1215/S0012-7094-73-04085-4
10.2140/pjm.1973.49.229
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References CIT0001
CIT0003
Thurber E.G. (CIT0005) 1973; 49
CIT0002
Tsai Y.H. (CIT0008) 1985
CIT0004
Tsai Y.H. (CIT0007) 1985
CIT0006
CIT0009
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  doi: 10.1090/S0002-9904-1939-07068-7
– ident: CIT0002
  doi: 10.1137/0210047
– volume-title: Algorithms for finding the shortest addition chain
  year: 1985
  ident: CIT0008
– ident: CIT0003
  doi: 10.1215/S0012-7094-62-02948-4
– ident: CIT0004
– volume-title: A study on some addition chain problems
  year: 1985
  ident: CIT0007
– ident: CIT0009
  doi: 10.1090/S0002-9939-1953-0054618-X
– ident: CIT0006
  doi: 10.1215/S0012-7094-73-04085-4
– volume: 49
  start-page: 229
  year: 1973
  ident: CIT0005
  publication-title: Pacific J. Math
  doi: 10.2140/pjm.1973.49.229
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Snippet In this paper, some mathematical properties of the shortest-length addition chain are found for certain integers whose binary patterns meet some special forms;...
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StartPage 117
SubjectTerms Addition Chain
big step
double step
F.1.3 [Complexity Classes]-relations among complexity measures
F.2.1 [Numer-ical Algorithms and Problem Complexity]-number-theoretic computations
F.l.l [Computation by Abstract Devices]
G.l [Numerical Analysis]-Computer Arithmetic
long-five
Models of Computation-computability theory
short-five
small step
special four
the shortest-length addition chain
Title A study of some addition chain problems
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