In Search of a Compositional Theory of Self-Stabilization
My quest for a principled solution for metastable failures has taken me back to my roots on self-stabilization, as this recent paper related the problem to composition of self-stabilizing systems. But, my literature search for recent work on composing self-stabilizing systems didn't yield anything useful. The layered stabilization idea was already in place by the early 2000s, and nothing fundamental seems to have been added since. Frustrating. So I decided to attack the problem using the concrete example I have. I had composed a rely-guarantee TLA+ model of a retry storm as two components with contracts . That model reproduces metastable failure because the composition that worked from good states failed to work when a large shock removes the base case that let the two conditions hold each other up. Searching for rely-guarantee based composition from every state, turned up a 2017 control theory paper by Kim, Arcak and Seshia, "A Small Gain Theorem for Parametric Assume-Gua...