From State to Link-Register Model: A transformer for Self-Stabilizing Distributed Algorithms

In the link-register model, there is a delay between the time an action is taken and the time an adjacent node is informed of the resulting modification. This delay provides an opportunity to study the asynchronism induced by communications in distributed systems. Read/write atomicity, the most restrictive model in this category, permits only node-to-node communications. The unfair distributed daemon tops it off by being able to postpone a communication for arbitrarily long (precisely, until the algorithm can take no other move). This paper proposes a transformer to convert a self-stabilizing algorithm from the state to the link-register model. In the worst case, one move of the self-stabilizing algorithm in the state model can generate $\Delta$ rounds in the transformed algorithm in the linkregister model (where $\Delta$ is the maximum degree of the graph). This transformer is based on another transformer that goes from the state model to a slightly modified version of the link-register model, called the strong-link-register model, in which a node can read in its own registers. This transformation comes with a $O(\Delta )$ factor cost.