TY - JOUR

T1 - Parallel and sequential transformations on digital images

AU - Yamashita, Masafumi

N1 - Funding Information:
Acknowledgements--The authorw ishest o thank President N. Honda and Prof. T. Ibarakio f ToyohashUi niversityo f Technologayn dP rofsY . Inagakai ndJ . Toriwakio fNagoya Universityfo r manyh elpfuld iscussions. This work wasp artiallys upportebdy a ScientifiRc esearch Grant-in-Aidfr om the Ministryo f EducationS, ciencea nd CultureJ,a pan.

PY - 1985

Y1 - 1985

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

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

M3 - Article

AN - SCOPUS:0021892066

SN - 0031-3203

VL - 18

SP - 31

EP - 41

JO - Pattern Recognition

JF - Pattern Recognition

IS - 1

ER -