The P vs NP Problem: The Millennium Prize Challenge
An in-depth exploration of one of computer science's most famous open questions. What does it mean for a problem to be efficiently solvable vs. efficiently verifiable?
The CookβLevin Theorem: Birth of NP-Completeness
How Stephen Cook and Leonid Levin revolutionized theoretical computer science by proving the first NP-complete problem, laying the groundwork for modern complexity classes.
Complexity Classes: P, NP, PSPACE, and Beyond
A comprehensive guide to the hierarchy of complexity classes, their relationships, containment proofs, and open questions in computational theory.
Polynomial-Time Reductions & NP-Hardness
Understanding how problems are transformed into one another to prove computational hardness. Step-by-step examples of Karp and Turing reductions.
Quantum Complexity: BQP and the Future of Computation
How quantum mechanics reshapes complexity theory. Exploration of BQP, quantum supremacy claims, and the limits of quantum advantage.
Complexity Theory in Modern Cryptography
Why public-key cryptography relies on the assumption that P β NP. Exploring one-way functions, trapdoors, and post-quantum cryptographic standards.