### Abstract

Reductions transform binary pictures only by changing some black points to white ones. Parallel reductions can alter a set of black points simultaneously, while a sequential reduction traverses the black points of a picture, and changes the actually visited single point if the considered deletion rule is satisfied. Two reductions are called equivalent if they produce the same result for each input picture. General-simple deletion rules yield pairs of equivalent topology-preserving parallel and sequential reductions in arbitrary binary pictures. This paper bridges P-simple points and general-simple deletion rules: we show that some deletion rules that delete P-simple points are general-simple, and each point deleted by a general-simple deletion rule is P-simple.

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 | 143-153 |

Number of pages | 11 |

Volume | 9647 |

ISBN (Print) | 9783319323596 |

DOIs | |

Publication status | Published - 2016 |

Event | 19th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2016 - Nantes, France Duration: Apr 18 2016 → Apr 20 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 9647 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 19th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2016 |
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Country | France |

City | Nantes |

Period | 4/18/16 → 4/20/16 |

### Fingerprint

### Keywords

- Equivalent reductions
- General-simple deletion rules
- P-simple points
- Topology preservation

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 9647, pp. 143-153). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9647). Springer Verlag. https://doi.org/10.1007/978-3-319-32360-2_11

**P-simple points and general-simple deletion rules.** / Palágyi, K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 9647, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9647, Springer Verlag, pp. 143-153, 19th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2016, Nantes, France, 4/18/16. https://doi.org/10.1007/978-3-319-32360-2_11

}

TY - GEN

T1 - P-simple points and general-simple deletion rules

AU - Palágyi, K.

PY - 2016

Y1 - 2016

N2 - Reductions transform binary pictures only by changing some black points to white ones. Parallel reductions can alter a set of black points simultaneously, while a sequential reduction traverses the black points of a picture, and changes the actually visited single point if the considered deletion rule is satisfied. Two reductions are called equivalent if they produce the same result for each input picture. General-simple deletion rules yield pairs of equivalent topology-preserving parallel and sequential reductions in arbitrary binary pictures. This paper bridges P-simple points and general-simple deletion rules: we show that some deletion rules that delete P-simple points are general-simple, and each point deleted by a general-simple deletion rule is P-simple.

AB - Reductions transform binary pictures only by changing some black points to white ones. Parallel reductions can alter a set of black points simultaneously, while a sequential reduction traverses the black points of a picture, and changes the actually visited single point if the considered deletion rule is satisfied. Two reductions are called equivalent if they produce the same result for each input picture. General-simple deletion rules yield pairs of equivalent topology-preserving parallel and sequential reductions in arbitrary binary pictures. This paper bridges P-simple points and general-simple deletion rules: we show that some deletion rules that delete P-simple points are general-simple, and each point deleted by a general-simple deletion rule is P-simple.

KW - Equivalent reductions

KW - General-simple deletion rules

KW - P-simple points

KW - Topology preservation

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U2 - 10.1007/978-3-319-32360-2_11

DO - 10.1007/978-3-319-32360-2_11

M3 - Conference contribution

SN - 9783319323596

VL - 9647

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 143

EP - 153

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -