P vs NP

If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in "creative leaps," no fundamental gap between solving a problem and recognizing a solution once it's found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss. -- Scott Aaronson

Simplicity is the final achievement. After one has played a vast quantity of notes and more notes, it is simplicity that emerges as the crowning reward of art. -- Chopin

One day, I will find the right words, and they will be simple. -- Jack Kerouac

Hard to Compute, Simple to Verify

• But relaxing the definition of "hard to compute, simple to verify" lets us make some interesting analogies across different emerging technologies.
• There's public-key cryptography, which relies on things hard to compute, easy-to-verify problems like factorization of large integers, or elliptic curve cryptography
• There are also zero-knowledge proofs, which let counterparties prove that they know ng without revealing the actual secret
• Before LLMs, generating the associated image took time if you were given a prompt. A talented artist could take a few hours (minutes, days, etc.) to create a polished piece. Once created, it would be easy to verify if it fits the criteria - is this an image of a horse wearing sunglasses?
• There are no problems that are easy to compute yet hard to verify. If such a problem existed, you could just re-run the computation again.

One such thing of can be tracking the time-based hash , but this is only true depending on the definition of . If verifying means giving input and comparing the output, yes, it is easy. It will be hard if verifying includes the information comparing the production. But then again, it also falls into another problem.