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Hilbert's Tenth Problem in Coq (Extended Version) [article]

Dominique Larchey-Wendling, Yannick Forster
2022 arXiv   pre-print
Additionally, we prove the reverse direction and show that every Diophantine relation is recognisable by μ-recursive functions and give a certified compiler from μ-recursive functions to Minsky machines  ...  We formalise the undecidability of solvability of Diophantine equations, i.e. polynomial equations over natural numbers, in Coq's constructive type theory.  ...  Acknowledgements We would like to thank Gert Smolka, Dominik Kirst, and Simon Spies for helpful discussion regarding the presentation.  ... 
arXiv:2003.04604v5 fatcat:xstpu6zkovh7zpoki3rlkkeedu

Synthetic Undecidability of MSELL via FRACTRAN Mechanised in Coq

Dominique Larchey-Wendling, Naoki Kobayashi
2021
We present an alternate undecidability proof for entailment in (intuitionistic) multiplicative sub-exponential linear logic (MSELL).  ...  We use this system called non-deterministic two counters Minsky machines to describe and compare both the legacy reduction to linear logic, and the more recent reduction to MSELL.  ...  [17] gave a first proof of the undecidability of propositional linear logic (LL) via a many-one reduction from "and-branching two-counter machines without zero-test, " a variant of Minsky machines extended  ... 
doi:10.4230/lipics.fscd.2021.18 fatcat:a3zmawbm4be53kxbc4z2kmbi74

Computability in constructive type theory [article]

Yannick Forster, Universität Des Saarlandes
2022
We identify a notion of synthetic undecidability relative to a fixed halting problem, allowing axiom-free machine-checked proofs of undecidability.  ...  We introduce a certifying extraction framework and analyse an axiom stating that every function of type → is L-computable. This thesis is a product of more than seven years of research.  ...  Post correspondence problem [81]Forster and Larchey-Wendling. "Certified Undecidability of Intuitionistic Linear Logic via Binary Stack Machines and Minsky Machines."  ... 
doi:10.22028/d291-35758 fatcat:deb5muacebhsnnmk5p25mgc7ia

Hilbert's Tenth Problem in Coq (Extended Version) [article]

Dominique Larchey-Wendling, Yannick Forster
2020
Additionally, we prove the reverse direction and show that every Diophantine relation is recognisable by $μ$-recursive functions and give a certified compiler from $μ$-recursive functions to Minsky machines  ...  We formalise the undecidability of solvability of Diophantine equations, i.e. polynomial equations over natural numbers, in Coq's constructive type theory.  ...  Acknowledgements We would like to thank Gert Smolka, Dominik Kirst, and Simon Spies for helpful discussion regarding the presentation.  ... 
doi:10.48550/arxiv.2003.04604 fatcat:pzgqtujjybeebeighmoqp4xlmi

LIPIcs, Volume 15, RTA'12, Complete Volume [article]

Ashish Tiwari
2013
We thank Ashish Tiwari, Nachum Dershowitz, the referees, and the attendants of TeReSe and the TF-lunch seminar, for feedback and interesting discussions.  ...  the presentation of the final version.  ...  1 c 1 q, zero(c1), q : q 1 1 c 1 q 1 1 c 1 Figure 8 Encoding of a Minsky machine. node deletion, edge contraction and edge deletion rules.  ... 
doi:10.4230/lipics.rta.2012 fatcat:i53phqg7yvahdovzjpatxgb7hq