The acronym for directed acylic graphs is DAG, not DAO. That's also an incredibly vague thing to be "based on" and seems more like an appeal to "impressive technical sounding name that actually happens to be extremely trivial and something people learn about in a first year undergraduate mathematics course".
DAG and not DAO of course... The mathematical description is straightforward however the implementation (for example mining fee distribution) seems fairly complicated and loses a lot of the beauty of a blockchain. AFAIK Iota is the first serious attempt at running such a crypto currency.
