Is P=NP?
2 days ago
- #P-vs-NP
- #complexity-theory
- #cryptography
- Complexity theory classifies problems based on computational resources like time and space.
- Big-O notation categorizes algorithms by their growth rates (e.g., O(1), O(n), O(n²), O(2ⁿ)).
- P (Polynomial Time) problems are solvable quickly, while NP (Nondeterministic Polynomial Time) problems have verifiable solutions but may be hard to solve.
- NP-Complete problems are universal hard problems; solving one could solve all NP problems.
- NP-Hard problems are at least as hard as NP-Complete but may not be verifiable quickly.
- P=NP would collapse cryptography and revolutionize AI by making optimization problems trivial.
- Modern cryptography relies on one-way functions, which would become obsolete if P=NP.
- The author had a dream about P=NP, leading to existential reflections on digital security.