Hi, my name is Nnamdi Michael Okpala, and I’m a researcher passionate about solving problems efficiently. Today, I’m going to share how I minimized a state machine, and optimized an abstract syntax tree (AST) using something we’re all familiar with: a game of tennis.

Note that this technology is patented from data of references in formal documentation in of github repo.

The Problem: Keeping Track of Tennis Scores
Imagine you and I are playing a game of tennis. The goal is simple — to win. In tennis, the score progresses like this:

0 (Love)
15
30
40
Game Point (1)
Now let’s say you’re a professional tennis player, and I’m a complete beginner. We agree to play 5 games, and every time, you win all 5 games while I score nothing.

A program to track this game could be designed in two ways:

Program A: Keeping Track of Everything
Program A would track every single event during the game. It would record:

Each point you score.
Every time I fail to score (which is a lot).
All transitions from one state (score) to another.
For example:

Game 1:
You: 0 → 15 → 30 → 40 → 1 Point
Me: 0 → 0 → 0 → 0 → 0
Game 2, 3, 4, 5:
Similar redundant records.
This approach stores everything, even the fact that my score remains stuck at 0 (Love). It works, but it’s wasteful. It uses too much memory and spends unnecessary time keeping track of things that don’t change.

Program B: A Smarter Way
Now, let’s think smarter. Program B keeps track only of what matters:

It starts by recording the scores at 0 (Love).
It tracks when you score points and advances your score through 15, 30, 40, and 1 Point.
It doesn’t track my score every time because it knows I’m stuck at 0 (Love).
For example:

Game 1:
You: 0 → 15 → 30 → 40 → 1 Point
Game 2, 3, 4, 5:
Same efficient record.
This program is smaller, faster, and doesn’t waste time storing unnecessary information.

The Automaton and AST Connection
This tennis game is like a state machine — a system that moves between states based on input. In our case:

States: Scores like 0, 15, 30, 40, and 1 Point.
Transitions: Events like scoring a point.
In Program A, the state machine tracks all states and transitions, including redundant ones. In Program B, I applied minimization techniques to:

Combine Redundant States: For example, “Me at 0” is constant and doesn’t need to be tracked repeatedly.
Focus on Important Transitions: The program tracks only your scoring events.
Now, the AST (abstract syntax tree) represents the structure of these transitions. Imagine the AST as a tree where:

Each branch represents a transition.
Each node represents a state (like 15 or 30).
By optimizing the AST, I:

Removed unnecessary nodes (e.g., “Me at 0”).
Simplified the tree so it only showed meaningful transitions (your scoring path).
Why Does This Matter?
Minimizing the state machine and optimizing the AST saved both memory and computation time. The program became faster and leaner while still delivering the correct result: You win all 5 games.

The Bigger Picture
This idea isn’t just about tennis. It’s how we can make programs smarter and more efficient in real-world applications. Whether it’s managing network traffic, optimizing a website, or building AI systems, state minimization and AST optimization make everything run smoother.

So next time you’re watching a tennis match, think about how scores move between states — and remember that even in simplicity, there’s power.

Thanks for reading!