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Yo-Yo leader election algorithm

A TLA+ specification of a leader election algorithm in connected undirected graphs introduced by Nicola Santoro in chapter 3.8.3 of Design and Analysis of Distributed Algorithms, see also Wikipedia. The algorithm assumes that every node has a unique (integer) identity and works by orienting edges of the graph such that sources (nodes with only outgoing edges) correspond to candidates. It will then successively execute rounds consisting of two phases edge that serve to eliminate sources (and reorient edges) until only the node with the smallest identity remains a source and is a leader.

The module YoYoNoPruning contains the specification of the base algorithm. It stabilizes in a state where the graph contains a single source, but does not terminate, since no node can detect stabilization. The module MCYoYoNoPruning instatiates the algorithm for model checking a number of properties using TLC.

The module YoYoPruning adds a pruning step to the second phase of each round in order to remove useless edges and nodes of the graph until the only source becomes isolated and declares itself the leader, whereas all other nodes have become inactive. The module MCYoYoPruning serves for checking properties of this specification using TLC.

The module YoYoAllGraphs describes the same algorithm as YoYoPruning but performs it on all connected undirected graphs of a certain number of nodes specified as a parameter. It allows for the algorithm to be verified beyond a single fixed graph.

The modules depend on the community module UndirectedGraphs for checking connectedness of the graph.