Towards a Theory of Peer-to-Peer Computability

A peer-to-peer system is a distributed system with no physical or logical central authority. We give a formal model of a peer-to-peer system where agents communicate through read-modify-write registers that can be accessed by exactly two agents. For this model, we study so-called ordering decision tasks for wait-free agents. We show how agents can determine their position in a total linearizable order in the peer-to-peer model. We also show that electing a leader among the agents and finding a predecessor agent in the total ordering cannot be implemented without a central authority. Our peer-to-peer model is related to other models of distributed computing, specifically to concurrent objects in asynchronous shared memory and to switching (counting) networks.