Hilbert Meets Isabelle: Formalisation of the DPRM Theorem in Isabelle

EasyChair Preprint 152

Abstract

Hilbert's tenth problem, posed in 1900 by David Hilbert, asks for a general algorithm to determine the solvability of any given Diophantine equation. In 1970, Yuri Matiyasevich proved the DPRM theorem which implies such an algorithm cannot exist. This paper will outline our attempt to formally state the DPRM theorem and verify Matiyasevich's proof using the proof assistant Isabelle/HOL.

Keyphrases: DPRM Theorem, Diophantine equations, Hilbert's tenth problem, Isabelle, recursively enumerable

@booklet{EasyChair:152,
  author    = {Benedikt Stock and Abhik Pal and Maria Antonia Oprea and Yufei Liu and Malte Sophian Hassler and Simon Dubischar and Prabhat Devkota and Yiping Deng and Marco David and Bogdan Ciurezu and Jonas Bayer and Deepak Aryal},
  title     = {Hilbert Meets Isabelle: Formalisation of the DPRM Theorem in Isabelle},
  doi       = {10.29007/3q4s},
  howpublished = {EasyChair Preprint 152},
  year      = {EasyChair, 2018}}