, cf Sample Clauses

, cf. Fig. 3.1, although there we were dealing with the full nonlinear reaction equations. This is the topic we consider next.

, cf. [7, Cor. 1]). If the predicate InStableRoot(I) evaluates to R ƒ= ∅ at process p in round r, then ∀t ∈ I where t < r, it holds that p is a member of Rt, i.e., p ∈ R. ∈ − The following Corollary 2 reveals that, in a sufficiently long interval of rounds I = [r, s] with an I-vertex- stable root component RI , every member p R detects its membership in the [r, s D]-VSRC RI with a latency of at most D rounds (i.e., at the end of round r + D). | | − Corollary 2 ( [7, Cor. 2]). Consider an interval of rounds I = [r, s], with I = s r + 1 > D, such that there is a D-bounded vertex-stable root component RI. Then, from the end of round s on, a call to InStableRoot([r, s − D]) returns R at every process in R. Together, Corollaries 1 and 2 reveal that InStableRoot(.) precisely characterizes the caller’s actual membership in the [r, s − D]-VSRC RI in the communication graphs from the end of round s on.