How-To on Amir Pourmand

How to model any DFA using SQL

Fri, 20 Feb 2026 00:00:00 +0000

The Problem

This was one of the challenges I had to handle recently. I wanted to model a Definitive Finite Automata (DFA) using SQL. This reminded me of one of the courses I took in my bachelors (+). This is where I understood how to use DFA for a SQL problem which at first, seems unsolvable.

Let’s define the problem clearly. Note that this is a real-life business problem. I’m not talking about theory and a made-up problem.

Derive Most Math Trigonometry Formulas via Euler Identity

Wed, 03 Sep 2025 00:00:00 +0000

When I was in high school, I remember that I had to memorize all trigonometry formulas. I didn’t have a single way to resort to when I was locked.

Fortunately, As I will show here, most trigonometry formulas can be derived via simple algebraic modifications of Euler's Formula.

This way, any time we are locked and can’t remember what the formula was, we can simply derive it.

I have used some LLM to generate proofs. So, this is the only post ever I’ve used LLMs. But I had to tell.

Setting Up Caddy for Reverse Proxy is dead simple

Wed, 03 Jul 2024 00:00:00 +0000

I’ve recently found Caddy as a tool to assign urls to my docker services and I’m quite happy with it. I’ve done other reverse proxies like Nginx and Traefik in the past but they are too complicated for my needs.

Let’s start.

Let’s say that you want to assign your url like newservice.amirpourmand.ir to a service in a VM with a public IP address. I’ll go you through it.

Also, It has multiple benefits. The first one is that you don’t have to do IPs. You don’t have to deal with ugly IPs that may change in the future. You deal with Secure URLs. The second is that the connection is https.