### A Characterization of the Unary Regular Languages

A expected solution to a simple problem

### Intuition in Complexity Theory

Complexity is a unique field because most of the important problems are unsolved. There is a giant web of implications of open problems, their barriers, and their relations.

### Death of Recursive Functions, The Impact of Relativization

The importance of the Baker-Gill-Solovay result

### Why Circuits?

Lets explore the necessity and use of Circuits as a computational model, and their use in MPC.

Why I think twitter is such a powerful platform.

### Some of what I Read Staying at Home in 2021

Another long year stuck inside. I graduated finally, and got a real job!

### Why isn't One prime?

Who wrote these rules?

### I don't like Harry Potter

Theres a few reasons. My first and main reason is the fans. People who read harry potter don’t seem to read any other non-fiction. I realized that this was true of me as well. I feel like it prevented me from finding multiple, more interesting stories than just one series

### The Bitconnect Story

For the bitcoin class, I usually get to give one lecture. I use this time to present some blockchain case studies. Specifically, this story.

### Some of what I Read Staying at Home in 2020

It has been a really long year, forced inside. Since I don’t have to bike to an office everyday, I found myself with a lot more time for reading. Here is some of what I read this year, mostly in the order that I read it.

The fact that there is no polynomial time integer factorization algorithm is something that will never not be suprising to me. All of the related problems are polytime. Primality testing is polytime. GCD is polytime. So why not integer factorization? Perhaps a polytime integer factorization algorithm exists based on GCD or on primality testing.

### A poop eating analogy found in information theory

Recall Kolmogorov complexity. Consider the following problem, which I came up for the honors section of the complexity class:

### Diogenes and Definitions

What makes a definition a good one?

### A Wrong Random Oracle Assumption

The random oracle assumption is a useful tool in cryptographic proofs, and this is about a mistake I made on its technicalities.

### Computational Indistinguishability is an Equivalence Relation.

I have not seen this anywhere in other sources so I thought I would write it up. It is actually not that important. Usually people only care about transitivity.

### A simple proof that took me a year.

Puzzle cubes are cool because its like holding a real algebraic object in your hand.

### Math over Magic

The world is a lot more boring when you realize somethings can’t exist.

### A Mathematician's Keyboard

I have been needing a use for an extra keyboard I had sitting in the closet.

### Chromebook Pixel and Arch Linux

I bought a Chromebook Pixel from 2013 during the Summer of 2016, since I wanted a new laptop, and these had deprecated in value incredibly considering they were $1200-1500 when they launched. I picked up the 64GB model for about$400. There are a lot of issues with this laptop and maybe I won’t do the same thing again. The display is incredibly bright and the image can often burn in if left on for too long. There is basically no cooling on this machine, so it was constantly at 85 celsius (I found a fix for this later) and the battery life was pretty terrible. My old C720, I could easily get 12 or 13 hours out of the thing. I have to charge this every day and be lucky to get 4 hours. Maybe I was just spoiled. I do like the 4:3 aspect ratio. It makes having two windows that partition the screen vertically more comfortable on a laptop. The resolution is also somewhat wasted on me. The fonts I mostly use are usually all monospaced and pixel perfect, so I don’t see an upgrade for 95% of what I do on this machine, but PDFs and webpages look like real paper, which is kinda neat I guess.

### bc is a terrible calculator

I’ve been messing around with some terminal based calculators. For my cryptography class, we had to do some huge computations. Ive noticed that GNU bc is actually pretty slow at this:

### One of my favorite integrals.

One of the counter-examples that was proposed by Cauchy to LaGrange’s functional idea was $e^{-x^2}$. This function, when integrated only has a series solution that cannot be represented in some closed form. You can however, evaluate it as a definite integral from $-\infty$ to $\infty$.