Posts

Production Index

Last edited: August 8, 2025

This is a work-in-progress page listing all of my production projects.

Fireside: Blog

Fireside Index

20MinuteRants: Blog

https://medium.com/20minuterants

(finished) Project80: Podcast

See .

(finished) Yappin: Podcast

https://anchor.fm/yappin/

Productivity Starter Pack

Last edited: August 8, 2025

So you wanted to be productive?

Go do stuff. Stop reading. Get crap done.

… … …

Wait, you are still here? Well, given that you are sticking around, we might as well discuss some tooling that may help you in organizing your work. By all means I don’t think this is a complete list, many of these have intersecting features; think of this as more a survey of the field—

products and quotients, the intuition

Last edited: August 8, 2025

We mentioned this in class, and I figured we should write it down.

So, if you think about the Product of Vector Space:

\begin{equation} \mathbb{R} \times \mathbb{R} \end{equation}

you are essentially taking the \(x\) axis straight line and “duplicating” it along the \(y\) axis.

Now, the opposite of this is the quotient space:

\begin{equation} \mathbb{R}^{2} / \left\{\mqty(a \\ 0): a \in \mathbb{R} \right\} \end{equation}

Where, we are essentially taking the line in the \(x\) axis and squish it down, leaving us only the \(y\) component freedom to play with (as each element is \(v +\left\{\mqty(a \\ 0): a \in \mathbb{R} \right\}\)).

Prof. Xin Liu

Last edited: August 8, 2025

programatically compiling RegEx to DFA

Last edited: August 8, 2025

A high level sketch:

Another High Level Sketch

Step 1: Write some RegExps

Do that.

Step 2: Construct R

For regular expressions you have defined for keywords, identifies, numbers, etc… We want to construct an uber union regular expression:

\begin{align} R &= \text{Keyword} + \text{Identifier} + \text{Number} + \dots \\ &= R_1 | R_2 | R_3 | \dots \end{align}

Step 3: Tokenization

For input \(x_1, …, x_{n}\), for \(i \in 1 …n\) inclusive, we check: