### Abstract

In this paper, the relation between parallel and sequential algorithms is discussed. We regard algorithms as definitions of transformations and investigated the relation between the sets of transformations defined by parallel and sequential algorithms. Three problems are treated mainly. The problems and the results for the problems may be summarized as follows. (1) Characterization of transformations which are both parallel and sequential-A necessary and sufficient condition for a transformation to be both parallel and sequential has been established. (2) Equivalence problems-The equivalence problem for two algorithms, one of which is parallel, is decidable, hence, the equivalence problem for two sequential algorithms is undecidable, i.e. an algorithm for deciding whether or not two given algorithms, one of which is parallel, define the same transformation has been presented. However, we have shown there is no algorithm for deciding whether or not two given sequential algorithms define the same transformation. (3) Translation problems-An algorithm for translating a parallel (sequential) algorithm into an equivalent sequential (parallel) algorithm has been presented.

Original language | English |
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Pages (from-to) | 31-41 |

Number of pages | 11 |

Journal | Pattern Recognition |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1985 |

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### All Science Journal Classification (ASJC) codes

- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Artificial Intelligence

### Cite this

*Pattern Recognition*,

*18*(1), 31-41. https://doi.org/10.1016/0031-3203(85)90004-4

**Parallel and sequential transformations on digital images.** / Yamashita, Masafumi.

Research output: Contribution to journal › Article

*Pattern Recognition*, vol. 18, no. 1, pp. 31-41. https://doi.org/10.1016/0031-3203(85)90004-4

}

TY - JOUR

T1 - Parallel and sequential transformations on digital images

AU - Yamashita, Masafumi

PY - 1985/1/1

Y1 - 1985/1/1

N2 - In this paper, the relation between parallel and sequential algorithms is discussed. We regard algorithms as definitions of transformations and investigated the relation between the sets of transformations defined by parallel and sequential algorithms. Three problems are treated mainly. The problems and the results for the problems may be summarized as follows. (1) Characterization of transformations which are both parallel and sequential-A necessary and sufficient condition for a transformation to be both parallel and sequential has been established. (2) Equivalence problems-The equivalence problem for two algorithms, one of which is parallel, is decidable, hence, the equivalence problem for two sequential algorithms is undecidable, i.e. an algorithm for deciding whether or not two given algorithms, one of which is parallel, define the same transformation has been presented. However, we have shown there is no algorithm for deciding whether or not two given sequential algorithms define the same transformation. (3) Translation problems-An algorithm for translating a parallel (sequential) algorithm into an equivalent sequential (parallel) algorithm has been presented.

AB - In this paper, the relation between parallel and sequential algorithms is discussed. We regard algorithms as definitions of transformations and investigated the relation between the sets of transformations defined by parallel and sequential algorithms. Three problems are treated mainly. The problems and the results for the problems may be summarized as follows. (1) Characterization of transformations which are both parallel and sequential-A necessary and sufficient condition for a transformation to be both parallel and sequential has been established. (2) Equivalence problems-The equivalence problem for two algorithms, one of which is parallel, is decidable, hence, the equivalence problem for two sequential algorithms is undecidable, i.e. an algorithm for deciding whether or not two given algorithms, one of which is parallel, define the same transformation has been presented. However, we have shown there is no algorithm for deciding whether or not two given sequential algorithms define the same transformation. (3) Translation problems-An algorithm for translating a parallel (sequential) algorithm into an equivalent sequential (parallel) algorithm has been presented.

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UR - http://www.scopus.com/inward/citedby.url?scp=0021892066&partnerID=8YFLogxK

U2 - 10.1016/0031-3203(85)90004-4

DO - 10.1016/0031-3203(85)90004-4

M3 - Article

AN - SCOPUS:0021892066

VL - 18

SP - 31

EP - 41

JO - Pattern Recognition

JF - Pattern Recognition

SN - 0031-3203

IS - 1

ER -