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.
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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 -