A guarantee that a system will continue to provide data, and that no centralized authority can shut down its services.
For distributed systems, liveness means that a protocol is able to exchange messages among nodes, with the nodes successfully coming to a consensus.
This means that a system has liveness guaranteed.
Blockchains are regularly trying to determine which history of transactions is accurate, rather than the messages itself.
Distributed systems have a degree of correctness, and this involves an ordering of transactions. There are two elements involved in this — liveness and safety.
Liveness guarantees that good things will happen eventually, meaning there is no timeframe for these things to happen.
Termination of a distributed computation is one of many examples of liveness.
Liveness is the guarantee that all validators will reach some consensus on a value.
This can be thought of as the guarantee that no two validators will be in disagreement and reach different values.
Conversely, safety is a guarantee that nothing bad will happen.
For example, Bitcoin's use of the Nakamoto Consensus means that there is an emphasis on liveness on Bitcoin's blockchain.
The history and the expected history will be the same if nodes were honest.
A node which is a copy of the ledger operated by a participant of the blockchain network should not show different values when compared to another node.
Two nodes yielding different values represents a problem.
Nodes must reach agreement on what the next block should include.