## Abstract

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.

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 |