  In the fully-anonymous (shared-memory) model, inspired by a biological
setting, processors have no identifiers and memory locations are anonymous.
This means that there is no pre-existing agreement among processors on any
naming of the memory locations. In this work, we ask fundamental questions
about the fully-anonymous model in the hope to obtain a better understanding of
the role of naming and anonymity in distributed computing.
  First, we ask what it means to solve a task under processor anonymity. With
tasks such as renaming, the traditional notion obviously does not apply.
Instead of restricting ourselves to colorless tasks, we propose using the
notion of group solvability, which allows transferring any task to
processor-anonymous models.
  Second, the difficulty with anonymity is that processors can hardly avoid
covering and then overwriting each other's writes, erasing information written
by their predecessors. To get to the bottom of this phenomenon, we ask what
system configurations are stable when processors keep reading and writing ad
infinitum. Resolving this question leads us to a wait-free solution to the
snapshot task, which then allows us to solve renaming and obstruction-free
consensus.
