#theory

3 articles

P vs NP

Why verifying a solution and discovering one look like utterly different tasks, what NP-completeness says about that gap, and why fifty years of effort has not settled the most important open question in computing.

10 min read·Jul 12, 2026

Computer Science

The Halting Problem

Why no program can decide whether another program halts, how Turing's diagonal argument proves it, and what undecidability means for the tools that check your code.

10 min read·Jul 9, 2026

Computer Science

Finite Automata and Regular Expressions

How a regular expression compiles into a tiny memoryless machine, why that makes it fast, and why it provably cannot match balanced brackets.

10 min read·Jul 6, 2026