Abstract This paper describes the formal verification of NP-hardness reduction functions two key problems relevant in algebraic lattice theory: closest vector problem and shortest problem, both infinity norm. The formalization uncovered a number with existing proofs literature. how these were corrected formalization. work was carried out proof assistant Isabelle.

This paper provides a meta-analysis of the impact business formalization on performance. We exploit meta-dataset 1,271 estimates derived from 20 studies available until October 2019. The analysis reveals that is associated with fairly small benefits take time to materialize. then exploited difference between policy-induced and self-induced investigating underlying effects, publication bias, sou...

Summary In this article, we formalize the theorems about orthogonal decomposition of Hilbert spaces, using Mizar system [1], [2]. For any subspace S a space H , vector can be represented by sum in and to S. The formalization complements spaces has been stored Mathematical Library [4]. We referred [5] [6] formalization.