  Gossip protocols aim at arriving, by means of point-to-point or group
communications, at a situation in which all the agents know each other secrets.
Recently a number of authors studied distributed epistemic gossip protocols.
These protocols use as guards formulas from a simple epistemic logic, which
makes their analysis and verification substantially easier.
  We study here common knowledge in the context of such a logic. First, we
analyze when it can be reduced to iterated knowledge. Then we show that the
semantics and truth for formulas without nested common knowledge operator are
decidable. This implies that implementability, partial correctness and
termination of distributed epistemic gossip protocols that use non-nested
common knowledge operator is decidable, as well. Given that common knowledge is
equivalent to an infinite conjunction of nested knowledge, these results are
non-trivial generalizations of the corresponding decidability results for the
original epistemic logic, established in (Apt & Wojtczak, 2016).
  K. R. Apt & D. Wojtczak (2016): On Decidability of a Logic of Gossips. In
Proc. of JELIA 2016, pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2.
