A Formal Proof of Complexity Bounds on Diophantine Equations
5 hours ago
- #Diophantine Equations
- #Formal Verification
- #Isabelle/HOL
- Presents a universal construction of Diophantine equations with bounded complexity in Isabelle/HOL.
- Discusses Hilbert's Tenth Problem and its undecidability for arbitrary Diophantine equations.
- Highlights the open problem status for rational numbers and bounded complexity cases.
- Introduces the concept of universal pairs (ν, δ) for Diophantine equations.
- Details formal verification efforts in Isabelle, including extensions to multivariate polynomials and number theory.
- Describes metaprogramming infrastructure for handling complex multivariate polynomial definitions.
- Reflects on the collaborative benefits between mathematicians and computer scientists in formalizing research.