Radix is built on a combined architecture and consensus algorithm called Tempo, which is fully outlined in the Tempo white paper that can be found here: http://bit.ly/2ADK8LA
The aim of Tempo is to create a secure and reliable consensus on a decentralized public ledger. To do this it must be:
Asynchronous - any process on the network can start or end whenever it needs to - e.g. it does not need to wait for a “block” to be mined.
Highly concurrent - many processes can be done simultaneously, without bottlenecks - e.g. there is not a limit to the number of transactions that can be fit into a “block”
Scalable - there is not an upper limit restricting the total throughput of the network, such as the limits CAP Theorem puts on Blockchains and DAGs.
To achieve this, Tempo relies on a two simple ideas, and one logical leap:
The use of a basic digital clock called a “logical clock”
Telling your neighbors what has been happening, a process called “Gossip”
To stop double spends across shards, your shard address should be based on your wallet public key
A logical clock is a counter that is incremented by 1 every time something new happens. On Radix, “something new” is when one Node speaks to another in the Radix network. This gives every Node their own relative time, based on network activity, and one they can use to create a simple order of events.
Gossip protocols are well established in computer science and are one of the fastest ways in which information can be reliably shared across a network. It works simply by a Node choosing a couple of other Nodes to tell something new to, and they, in turn, tell two other Nodes, and so on and so on. This causes information to spread at an exponential rate.
On Tempo, we add the Node logical clocks, signed by the Nodes in question, to the gossip they are spreading around the network. This allows everyone to see both new information, and at what logical clock time that information was seen by other members of the network.
To allow high scalability a Tempo ledger is split into a very large shard space, allowing a huge degree of concurrency. To avoid a double spend across any of the shards, the shard a wallet lives on is determined by its public key. This makes sure that any spend from a wallet will always start on the same shard.
When combined with the logical clocks and gossip, this Tempo to always find the total ordering of related events, allowing double spends to be quickly detected and ignored.