### Abstract

In this paper, we describe a formalized theory of size-optimal sorting networks. From this formalization we extract a certified checker that successfully verifies computer-generated proofs of optimality on up to 8 inputs. The checker relies on an untrusted oracle to shortcut the search for witnesses on more than 1.6 million NP-complete subproblems.

Original language | English |
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Title of host publication | Interactive Theorem Proving : 6th International Conference, ITP 2015, Nanjing, China, August 24-27, 2015, Proceedings |

Editors | Christian Urban, Xingyuan Zhang |

Publisher | Springer |

Publication date | 2015 |

Pages | 154-169 |

ISBN (Print) | 978-3-319-22101-4 |

ISBN (Electronic) | 978-3-319-22102-1 |

DOIs | |

Publication status | Published - 2015 |

Series | Lecture Notes in Computer Science |
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Volume | 9236 |

ISSN | 0302-9743 |

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### Cite this

*Interactive Theorem Proving: 6th International Conference, ITP 2015, Nanjing, China, August 24-27, 2015, Proceedings*(pp. 154-169). Springer. Lecture Notes in Computer Science, Vol.. 9236 https://doi.org/10.1007/978-3-319-22102-1_10

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*Interactive Theorem Proving: 6th International Conference, ITP 2015, Nanjing, China, August 24-27, 2015, Proceedings.*Springer, Lecture Notes in Computer Science, vol. 9236, pp. 154-169. https://doi.org/10.1007/978-3-319-22102-1_10

**Formalizing Size-Optimal Sorting Networks : Extracting a Certified Proof Checker.** / Cruz-Filipe, Luís; Schneider-Kamp, Peter.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Formalizing Size-Optimal Sorting Networks

T2 - Extracting a Certified Proof Checker

AU - Cruz-Filipe, Luís

AU - Schneider-Kamp, Peter

PY - 2015

Y1 - 2015

N2 - Since the proof of the four color theorem in 1976, computer-generated proofs have become a reality in mathematics and computer science. During the last decade, we have seen formal proofs using verified proof assistants being used to verify the validity of such proofs.In this paper, we describe a formalized theory of size-optimal sorting networks. From this formalization we extract a certified checker that successfully verifies computer-generated proofs of optimality on up to 8 inputs. The checker relies on an untrusted oracle to shortcut the search for witnesses on more than 1.6 million NP-complete subproblems.

AB - Since the proof of the four color theorem in 1976, computer-generated proofs have become a reality in mathematics and computer science. During the last decade, we have seen formal proofs using verified proof assistants being used to verify the validity of such proofs.In this paper, we describe a formalized theory of size-optimal sorting networks. From this formalization we extract a certified checker that successfully verifies computer-generated proofs of optimality on up to 8 inputs. The checker relies on an untrusted oracle to shortcut the search for witnesses on more than 1.6 million NP-complete subproblems.

U2 - 10.1007/978-3-319-22102-1_10

DO - 10.1007/978-3-319-22102-1_10

M3 - Article in proceedings

SN - 978-3-319-22101-4

T3 - Lecture Notes in Computer Science

SP - 154

EP - 169

BT - Interactive Theorem Proving

A2 - Urban, Christian

A2 - Zhang, Xingyuan

PB - Springer

ER -