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Proof of Stake

There is a variety of PoSs, which tell a lot about how a particular cryptoecosystem works.
PoS is different from PoW because it is a system in itself without clear coupling to external systems (unlike PoW which require huge computational resources, and therefore enrgy consumption). PoS is particularly interesting, because consensus acts like Maxwell demon by creating high-information content, low-entropy record of the transactions (or any other information). This is why PoS is particularly interesting from the information theory perspective, see the fourth theory in The Many Faces of Bitcoin.

Classification of various proof of stake mechanisms

Essential articles about Casper PoS for Ethereum

https://github.com/ethereum/wiki/wiki/Proof-of-Stake-FAQ

Initial explorations on full PoS proposal mechanisms -Casper by Buterin (Jan 2018)

A Proof of Stake Design Philosophy by Buterin (Dec 2016)

The History of Casper — Chapter 5 by Vlad Zamfir (Dec 2016)

Proof of Stake: How I Learned to Love Weak Subjectivity by Buterin (Nov 2014)

Tendermint

  • attached whitepaper Tendermint: Consensus without Mining by Jae Kwon]()

adapting an existing solution to the Byzantine Generals Problem

  • comparisons

Consensus Compare: Casper vs. Tendermint

The CAP Theorem in computer science returns the impossibility of providing more than 2 out of 3 guarantees in distributed data systems: availability, consistency, and partition tolerance. Chain-based PoS algorithms tend to choose availability over consistency, where having availability means that all transactions will be processed, but at the expense of a consistent state replicating across the network. BFT-based PoS algorithms, on the other hand, strictly choose consistency over availability.

Availability-consistency-partition is not the same as finality-large number of validators-overhead.

Zamfir's Triangle - Reasonably low latency to finality, reasonably large number of validators, and reasonably low overhead.

a good overview of technological trade-offs is MODELS FOR SCALING TRUSTLESS COMPUTATION including issues of open-source, censorship, and politics (see the figure from the article)
tradeoff

see also Zamfir remark and The History of Casper — Chapter 3

Tendermint is a BFT-based PoS design, Casper the Friendly Ghost is a chain-based PoS design, and Casper the Friendly Finality Gadget is a hybrid of the two.

Consensus Compare: Tendermint BFT vs. EOS dPoS

A Deep Look Into Cosmos — the Internet of Blockchains sept 2018

Objections

These objections are mainly of general character, nevertheless the fundamental questions remain unanswered.

Proof-of-Stake, Private Keys Attacks and Unforgeable Costliness the Unsung Hero

In my previous article, I discussed how PoS is less resilient than PoW in dealing with worst-case scenarios. In this article, I want to expand on worst-case scenario #3: private keys attacks.

What’s Wrong with Proof of Stake? June 2016

On Stake and Consensus 2015 by Andrew Poelstra

Another point is that the valuation of PoS cryptocurrency (if only medium-of-exchange) should be significantly lower than PoW by using "exchange theory of money", see the middle of this paper.

Proof of Space/Time which is a different PoS