Hi I wrote this based on their whitepaper and based on my research on the Byzantine method which the Antshares, now NEO famed "upgrade"?from the projects that came before it. Here is the link to that article you may find helpful.
https://btcmanager.com/antshares-flexes-a-tech-muscle-set-to-release-smart-contracts-for-everyone/And here is an excerpt from the article that gives an idea why Antshares / NEO is special.
" The Byzantine Alternative?
There is an alternative emerging called the distributed Byzantine Fault Tolerance algorithm (or dBFT) which is used by Antshares, the Shanghai-based blockchain startup technology company, as well as Hyperledger.
The term Byzantine Fault Tolerance (BFT) is named after the Byzantine General’s problem, or an intricate and complex system vulnerable to attack when sides do not agree on one thing. The BFT describes the challenge of achieving consensus in a distributed blockchain. Securing a publicly distributed blockchain with a Byzantine Fault Tolerance algorithm has a high tolerance even if under attack.
To secure blockchains, a distributed Byzantine Fault Tolerance algorithm recognizes two types of participants which are professional node operators, doing so to make money and regular users who are simply using the blockchain.
A dBFT blockchain achieves consensus via the specially appointed, professionally-operated nodes nominated by ordinary nodes through delegated voting. One of these special nodes will act as a "Chairman" for each newly forged block and broadcasts their version of the blockchain; if two thirds of the other nodes agree, consensus is reached. In the event, consensus is not reached, another node is appointed as "Chairman" until two thirds of the remaining nodes agree.
Consequently, the rate of transaction handling is much faster and more energy efficient than the alternatives..."
Hope it helps! !
