### 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 |
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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 | |

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) |
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Volume | 1350 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 8th Annual International Symposium on Algorithms and Computation, ISAAC 1997 |
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Country | Singapore |

City | Singapore |

Period | 12/17/97 → 12/19/97 |

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

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## Cite this

*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