When you are selling a pizza and accepting Bitcoin, usually you wait “for a while” before you “confirm the transaction” and deliver the pizza. You are cautious because a fraudulent user may double spend—use the same bill to pay two different vendors.
I finished listening to the book “Endure” by Alex Hutchinson. It is one of the most important books that I have read. I have had multiple important realizations from it.
Brain sets an expectation. Giving up is almost always a choice.
Brain sets an expectation. You know it or not, feel it or not, your brain sets an expectation at a physiological as well as a psychological level. Try as we may, the brain controls your actions (again, at both the physiological and psychological levels) so that you meet the expectation, but don’t exceed it.
Therefore, these expectations matter. Sometimes these expectations are conscious, in that we can spell them out. Other times, they are at a subconscious or even unconscious level. Are you aware of what you expect of yourself? Expect does not mean hope: what do you really, really expect of yourself?
I gave a talk in our seminar about the proof-of-work vs. the proof-of-stake blockchain paradigm. Although I don’t have an audio/video recording, here is a Google Slides rendering of my original Powerpoint slides. Some of the animations are out of place/order, but in general, it feels okay.
I intended this talk to be accessible in nature, so I intentionally skipped many details and strived not to flaunt any equation in it.
Advertised Summary: Bitcoin is a blockchain protocol where finalized transactions need a “proof of work”. Such protocols have been criticized for a high demand for computing power i.e., electricity. There is another family of protocols which deals with a “proof of stake”. In these protocols, the ability to make a transaction depends on your “stake” in the system instead of your computing power. In both cases, it is notoriously difficult to mathematically prove that these protocols are secure. Only a handful of provably secure protocols exist today. In this talk, I will tell a lighthearted story about the basics of the proof-of-work vs. proof-of-stake protocols. No equations but a lot of movie references.
Please enjoy, and please let me know your questions and comments.
In this note, we are going to state the PCP theorem and its relation to the hardness of approximating some NP-hard problem.
PCP Theorem: the Interactive Proof View
Intuitively, a PCP (Probabilistically Checkable Proof) system is an interactive proof system where the verifier is given random bits and he is allowed to look into the proof in many locations. If the string is indeed in the language, then there exists a proof so that the verifier always accepts. However, if is not in the language, no prover can convince this verier with probability more than . The proof has to be short i.e., of size at most . This class of language is designated as PCP[r(n), q(n)].
Theorem A (PCP theorem). Every NP language has a highly efficient PCP verifier. In particular,