Tags:integer programming, lattice problems, NP-hardness and verification

Abstract:

This paper describes the formal verification of NP-hardness 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.

Verification of NP-Hardness for Exact Lattice Problems