## Abstract

We introduce a concept of local computability for designing high‐speed parallel algorithms on fan‐in restricted models. A function is k‐locally computable if each subfunction sepends on only at most k input variables. If k is a constant independent of n, the number of input variables, we can construct an O(1) time parallel algorithm for F on a fan‐in restricted computation model. In order to realize the local computability, we use a redundant coding scheme. We show that a binary operation of any finite Abelian group is k‐locally computable under a redundant coding scheme, where k is a constant independent of the order of the group. We also show that we can design a redundant coding scheme for a residue ring Z_{m} of integers under which addition and multiplication can be performed in O(1) and O(log log log m) time, respectively, in parallel, when m is the product of the smallest r primes.

Original language | English |
---|---|

Pages (from-to) | 72-80 |

Number of pages | 9 |

Journal | Systems and Computers in Japan |

Volume | 18 |

Issue number | 12 |

DOIs | |

Publication status | Published - 1987 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Hardware and Architecture
- Computational Theory and Mathematics