I experience a difficulty in solving exercises in distributed algorithm. Below is the the exercise I try to solve, it looks like I miss basic idea.
Exercise. Consider a 15-processor asynchronous network with processors 0,…,14. The processors constantly run a synchronizer. Let $v$ and $v'$ be two processors in the network, and suppose that at a certain moment, the pulse counter at $v$ shows $p=27$. What is the range of possible pulse numbers at $v'$ in each of the following cases:
a) The network is a ring, $v$ is processor number 11, $v'$ is processor number 2 and the synchronizer used is $\alpha$.
Idea: if $v'$ hasn't sent any message up to pulse 27 of $v$, pulse of $v'$ is still 0, therefore lower bound of pulse of $v'$ is 0. The model of synchronizer is $\alpha$ it means every node informs all nodes about it's safe(v,p) state, hence I assume that $v'$ might be 11-2=9 pulses before $v$.
b) The network is a full balanced binary tree (4 levels), $v$ is the root, $v'$ is one of the leaves and the synchronizer used $\beta$.
Idea: $v'$ also might have pulse 27, in this case $v$ sends at speed of $v'$.
c) The same as in (b), except both $v$ and $v'$ are leaves.
Honestly, I am completely confused by this exercise, I wrote few ideas, but I don't have any understanding and any intuition behind the answers.
I will appreciate if someone show me the way how to solve such exercises.