Byteball need witnesses + POS. If the witnesses honest, DAG works in the fast mode. If the Byteball witnesses under 51 attack, DAG switch to POS algorithm (slow mode) until 51 attack will not be fixed and the new witnesses will not replace malicious ones.
Hi pineapple express,
What you call 51 attack isn't really possible with the Byteball DAG model because there is no miner and due to the serialized logic of partial orders and then of total orders.
Obviously, majority of witnesses could collude in attempt to rewrite history. Unfortunately for them, an attempt of rewriting history has severe consequences with the Byteball model because everybody is allowed to post/write units/data in the chain/database.
Indeed, every unit posted in the chain has a referenced parent and this parent a chain of referenced ancestors until the genesis unit. Alter the chain of a unit ancestors will create inevitabilly orphan units and potentially break the chain until the genesis unit.
Honnest witnesses can detect this kind of paradoxal events and choose a new chain as best chain. Worst, honnest witnesses will exclude dishonnest ones and communicate about these renegates publicly to be sure that community will exclude them definitively.
In plus, Byteball model tolerates 1 witness permutation that allows potential alternate histories/realities to coexist along the main chain. These alternate chains can be choose to handle the cataclismic event of rewriting attempt.
Eventually, the role of witnesses are to post units periodically every 100 non-witnesses main chain which will be used as lighthouses (or luminous witnesses) by non-witnesses. These navigational aids for non-witnesses allow them to choose the best chain/path until the genesis unit. So, witnesses can't rewrite non-witnesses posts and their "power" is very limited and mainly honorific.
By the way, everybody can run a witness node and set it as its own permuted witness with the possibility of keep the chain healty until the genesis unit with its own reality. Better, we can be the lighthouse of many ;-) Yes, we can be a non-official witness.
Bye