  In order to formalize Distributed Ledger Technologies and their
interconnections, a recent line of research work has formulated the notion of
Distributed Ledger Object (DLO), which is a concurrent object that maintains a
totally ordered sequence of records, abstracting blockchains and distributed
ledgers. Through DLO, the Atomic Appends problem, intended as the need of a
primitive able to append multiple records to distinct ledgers in an atomic way,
is studied as a basic interconnection problem among ledgers.
  In this work, we propose the Distributed Grow-only Set object (DSO), which
instead of maintaining a sequence of records, as in a DLO, maintains a set of
records in an immutable way: only Add and Get operations are provided. This
object is inspired by the Grow-only Set (G-Set) data type which is part of the
Conflict-free Replicated Data Types. We formally specify the object and we
provide a consensus-free Byzantine-tolerant implementation that guarantees
eventual consistency. We then use our Byzantine-tolerant DSO (BDSO)
implementation to provide consensus-free algorithmic solutions to the Atomic
Appends and Atomic Adds (the analogous problem of atomic appends applied on
G-Sets) problems, as well as to construct consensus-free Single-Writer BDLOs.
We believe that the BDSO has applications beyond the above-mentioned problems.
