Formulation of the addition-shift-sequence problem and its complexity

Akihiro Matsuura; Akira Nagoya

doi:10.1007/3-540-63890-3_6

Formulation of the addition-shift-sequence problem and its complexity

Akihiro Matsuura, Akira Nagoya

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Given a sequence of integers, what is the smallest number of additions and shifts needed to compute all integers starting with 1? This is a generalization of the addition-sequence problem which naturally appears in the multiplication of constants with a single variable and in its hardware implementation, and it will be called the addition-shift- sequence problem. As a fundamental result on computational complexity, we show that the addition-shift-sequence problem is NP-complete. Then, we show lower and upper bounds of the number of operations for some particular sequence, where some techniques specific to our model are demonstrated.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher	Springer Verlag
Pages	43-51
Number of pages	9
Volume	1350
ISBN (Print)	3540638903, 9783540638902
DOIs	https://doi.org/10.1007/3-540-63890-3_6
Publication status	Published - 1997
Externally published	Yes
Event	8th Annual International Symposium on Algorithms and Computation, ISAAC 1997 - Singapore, Singapore Duration: Dec 17 1997 → Dec 19 1997

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1350
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	8th Annual International Symposium on Algorithms and Computation, ISAAC 1997
Country	Singapore
City	Singapore
Period	12/17/97 → 12/19/97

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ASJC Scopus subject areas

Computer Science(all)
Theoretical Computer Science

Cite this

Matsuura, A., & Nagoya, A. (1997). Formulation of the addition-shift-sequence problem and its complexity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1350, pp. 43-51). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1350). Springer Verlag. https://doi.org/10.1007/3-540-63890-3_6

Formulation of the addition-shift-sequence problem and its complexity. / Matsuura, Akihiro; Nagoya, Akira.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1350 Springer Verlag, 1997. p. 43-51 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1350).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Matsuura, A & Nagoya, A 1997, Formulation of the addition-shift-sequence problem and its complexity. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1350, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1350, Springer Verlag, pp. 43-51, 8th Annual International Symposium on Algorithms and Computation, ISAAC 1997, Singapore, Singapore, 12/17/97. https://doi.org/10.1007/3-540-63890-3_6

Matsuura A, Nagoya A. Formulation of the addition-shift-sequence problem and its complexity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1350. Springer Verlag. 1997. p. 43-51. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-63890-3_6

Matsuura, Akihiro ; Nagoya, Akira. / Formulation of the addition-shift-sequence problem and its complexity. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1350 Springer Verlag, 1997. pp. 43-51 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Access to Document

10.1007/3-540-63890-3_6