  We consider operation of blockchain-based cryptocurrency in case of
partitioning. We define the Partitionable Blockchain Consensus Problem. The
problem may have an interesting solution if the partitions proceed
independently by splitting accounts. We prove that this problem is not solvable
in the asynchronous system. The peers in the two partitions may not agree on
the last jointly mined block or, alternatively, on the starting point of
independent concurrent computation. We introduce a family of detectors that
enable a solution. We establish the relationship between detectors. We present
the algorithm that solves the Partitionable Blockchain Consensus Problem using
our detectors. We extend our solution to multiple splits, message loss and to
partition merging. We simulate and evaluate the performance of detectors,
discuss the implementation of the detectors and future work.
