Verification of NP-hardness Reduction Functions for Exact Lattice Problems
This paper describes the formal verification of NP-hardness reduction functions of two key problems relevant in algebraic lattice theory: the closest vector problem and the shortest vector problem, both in the infinity norm. The formalization uncovered a number of problems with the existing proofs in the literature. The paper describes how these problems were corrected in the formalization. The work was carried out in the proof assistant Isabelle.
arXiv
BibTeX:
@inproceedings{KreuzerN-CADE23,author={Katharina Kreuzer and Tobias Nipkow},
title={Verification of {NP}-hardness Reduction Functions for Exact Lattice Problems},
booktitle="Automated Deduction --- CADE-29",editor={B. Pientka and C. Tinelli},
year=2023,publisher={Springer},series={LNCS},volume={14132},pages={?--?}}
Springer's final version
Isabelle formalization