Confluence
Confluence
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MultiwaySystem[{"AAB""ABBBAA"},{"AAABBB"},5,"EvolutionPlot"]
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LayeredGraphPlot[MultiwaySystem[{"AAB""ABBBAA"},{"AAABBB"},15,"StatesGraph","StateGraphLabels"None]]
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Confluence in Multiway Systems
Confluence in Multiway Systems
Confluence implies that every path from a given node will always eventually reconverge
Confluence implies that every path from a given node will always eventually reconverge
Or equivalently: every divergence eventually has an associated convergence
[[[The only way one knows this has failed is if there’s more than one node with out-degree 0]]]]
Strong confluence implies that every divergence has an associated convergence after just one step
Strong confluence implies that every divergence has an associated convergence after just one step
Definition: critical pairs are pairs of distinct states that can be reached from a single state
Definition: critical pairs are pairs of distinct states that can be reached from a single state
Notion of “divergence lifetime”
Notion of “divergence lifetime”
How long does it take for a divergence to eventually reconverge?
Strong confluence is equivalent to divergence lifetime of 1
Divergence lifetime distribution?
Consider the set of different flow rates into different branches
Consider the set of different flow rates into different branches