TY - GEN

T1 - Formulation of the addition-shift-sequence problem and its complexity

AU - Matsuura, Akihiro

AU - Nagoya, Akira

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84958037387&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958037387&partnerID=8YFLogxK

U2 - 10.1007/3-540-63890-3_6

DO - 10.1007/3-540-63890-3_6

M3 - Conference contribution

AN - SCOPUS:84958037387

SN - 3540638903

SN - 9783540638902

VL - 1350

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 43

EP - 51

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

T2 - 8th Annual International Symposium on Algorithms and Computation, ISAAC 1997

Y2 - 17 December 1997 through 19 December 1997

ER -