## Abstract

Matrix interpretations are widely used in automated complexity analysis. Certifying such analyses boils down to determining the growth rate of An for a fixed non-negative rational matrix A. A direct solution for this task involves the computation of all eigenvalues of A, which often leads to expensive algebraic number computations. In this work we formalize the Perron-Frobenius theorem. We utilize the theorem to avoid most of the algebraic numbers needed for certifying complexity analysis, so that our new algorithm only needs the rational arithmetic when certifying complexity proofs that existing tools can find. To cover the theorem in its full extent, we establish a connection between two different Isabelle/HOL libraries on matrices, enabling an easy exchange of theorems between both libraries. This connection crucially relies on the transfer mechanism in combination with local type definitions, being a non-trivial case study for these Isabelle tools.

Original language | English |
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Title of host publication | Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs |

Editors | Amy Felty, June Andronick |

Pages | 2-13 |

Number of pages | 12 |

ISBN (Electronic) | 9781450355865 |

DOIs | |

Publication status | Published - 8 Jan 2018 |

Event | 7th ACM SIGPLAN International Conference on Certified Programs and Proofs 2018 - Los Angeles, United States Duration: 8 Jan 2018 → 9 Jan 2018 Conference number: 7 https://conf.researchr.org/home/CPP-2018 |

### Conference

Conference | 7th ACM SIGPLAN International Conference on Certified Programs and Proofs 2018 |
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Abbreviated title | CPP 2018 |

Country/Territory | United States |

City | Los Angeles |

Period | 8/01/18 → 9/01/18 |

Internet address |