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.

## pl

posts related to computing and programming languages

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.