Generally, Pos(Proof of Stake) is algorithm using staked coin, and it does not use nonce calculation. Therefore it has following problems.
But by using least nonce calculation and mining ticket algorithm, it can solve them.
Ticket PoS Algorithm has mechanism to decide miner node by registered ticket order.
In order to mine a block and get reword, full nodes have to register a ticket, and wait for their turn.
The full node which has oldest ticket can mine a block without nonce calculation. When the block is mined, the ticket is consumed, and next ticket's turn comes.
On consuming the ticket, the full node can post a new ticket.
Sometimes, a full node whose ticket comes neglect generating a new block. Then, backup full node start to calculate nonce of the block.
The difficulty for the full nodes is different. Older node's difficulty is easier.
If the current node, which is oldest ticket does not mine before other nodes calculate nonce, it was assumed to be neglect that.
A node which posted a ticket can't post new ones before it was consumed. Therefore rich person can't put a lot of ticket in the blockchain.
In this algorithm, all of full nodes has same opportunity to mine a new block and get reword.
In order to generate a new block without getting turn, a full node have to calculate nonce.
Therefore the Nothing-at-Stake Problem in PoS does not occur.
