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I have the notion of a social network which is robust against malicious attacks from the outside. My vision is a system that is structurally built up as a distributed network of equal servers that operate on the same data and offer the identical services. Users should all interact on the same network, independent of the respective server they communicate with. The idea is to prevent (at least theoretically) every opportunity to bring the whole system down and to achieve a total failure of the whole service. Obviously the design of such a system is not trivial because of proper synchronization mechanisms. On the other hand there is the challenge to convey the participants to the appropriate servers. Hope you got my idea roughly.

The thing is that I only have a vague notion how such a system can function, and furthermore have seemingly successful passed over the relevant lectures about distributed systems in my cs studies. I'm therefore a little bit in a lack of an overview of relevant literature, scientific papers describing theoretical models and also real world examples.

Can anyone help me out with references, links and helpful explanations?

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To me, what you are looking for is the "replicated state machine" approach, which is a general method for implementing a fault-tolerant service by replicating servers and coordinating client interactions with server replicas.

You can first check the wiki: State machine replication and the survey paper Implementing Fault-Tolerant Services Using the State Machine Approach: A Tutorial.

For further reading, you may need to learn distributed consensus algorithm, especially the Paxos algorithm (for example, Paxos Made Simple).

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