  Perpetual exploration is a fundamental problem in the domain of mobile
agents, where an agent needs to visit each node infinitely often. This issue
has received lot of attention, mainly for ring topologies, presence of black
holes adds more complexity. A black hole can destroy any incoming agent without
any observable trace. In
\cite{BampasImprovedPeriodicDataRetrieval,KralovivcPeriodicDataRetrievalFirst},
the authors considered this problem in the context of \textit{ Periodic data
retrieval}. They introduced a variant of black hole called gray hole (where the
adversary chooses whether to destroy an agent or let it pass) among others and
showed that 4 asynchronous and co-located agents are essential to solve this
problem (hence perpetual exploration) in presence of such a gray hole if each
node of the ring has a whiteboard. This paper investigates the exploration of a
ring in presence of a ``byzantine black hole''. In addition to the capabilities
of a gray hole, in this variant, the adversary chooses whether to erase any
previously stored information on that node. Previously, one particular initial
scenario (i.e., agents are co-located) and one particular communication model
(i.e., whiteboard) are investigated. Now, there can be other initial scenarios
where all agents may not be co-located. Also, there are many weaker models of
communications (i.e., Face-to-Face, Pebble) where this problem is yet to be
investigated. The agents are synchronous. The main results focus on minimizing
the agent number while ensuring that perpetual exploration is achieved even in
presence of such a node under various communication models and starting
positions. Further, we achieved a better upper and lower bound result (i.e., 3
agents) for this problem (where the malicious node is a generalized version of
a gray hole), by trading-off scheduler capability, for co-located and in
presence of a whiteboard.
