  Directed Acyclic Graph (DAG) based Distributed Ledgers can be useful in a
number of applications in the IoT domain. A distributed ledger should serve as
an immutable and irreversible record of transactions, however, a DAG structure
is a more complicated mathematical object than its blockchain counterparts, and
as a result, providing guarantees of immutability and irreversibility is more
involved. In this paper, we analyse a commonly discussed attack scenario known
as a parasite chain attack for the IOTA Foundation DAG based ledger. We analyse
the efficacy of IOTA core MCMC algorithm using a matrix model and present an
extension which improves the ledger resistance to these attacks.
