What is it?

Applet displaying a beautiful rotating plot of four metrics on 2000 Boolean expressions

My doctoral research involved boolean expressions, and one of the questions I was investigating involved predictive metrics.

I found that a metric that I called 'degree of coincidence', based upon an aspect of the structure of the expression, was a great predictor for whether expressions were tautologies or contradictions.

The Java applet (hopefully) running above displays four pieces of information about several hundred randomly generated boolean expressions.

The color of each dot is the expression's logical class: tautologies, contradictions, and expressions that are both satisfiable and falsifiable.

This is a static view of similar data:

In this view, the horizontal axis is the log₁₀ of the number of clauses in the Conjunctive Normal Form (CNF) equivalent of the expression and the vertical axis is the log₁₀ of the number of clauses in the Disjunctive Normal Form (DNF) equivalent of the expression.

Gorgeous.

The third spatial dimension, projecting out from the screen for the static view, is the Degree of Coincidence for the expression. I'll define this metric much later when I start to present some of my work on boolean expressions.

The important thing to note is how well the Degree of Coindidence separates tautologies from contradictions.

For fun: If you click on the left side of the spinning cluster, it will slow down; if you click on the right side of the spinning clust, it will speed up. Repeat.

This is one of my favorite things.

All Rights Reserved.