WJD Open Notebook

This post details the steps I use to update or install the latest version of the Java Development Kit (JDK) on my Linux systems.

Suppose the lattice shown below is a congruence lattice of an algebra.

Conjecture: If the three $\alpha_i$'s pairwise permute, then all pairs in the lattice permute.

It is not hard to see that 3-SAT reduces to the problem of deciding whether all coatoms in a certain partition lattice are contained in the union of a collection of certain principal filters. Therefore, the latter problem, which we will call the covered coatoms problem (CCP), is NP-complete. In this post we simply define CCP. Later we check that 3-SAT reduces to CCP, and then develop some ideas about constructing a feasible algorithm to solve CCP.

The questions below appeared on an online test administered by Jane Street Capital Management to assess whether a person is worthy of a phone interview.

This post includes some links to notes about various topics related (sometimes tangentially) to programming languages. These are very rough, often unfinished, and not really meant for public consumption. However, I don't care if others look at them. There is no personal or confidential information on these pages.