Concurrent use of write-once memory

We consider the problem of implementing general shared-memory objects on top of write-once bits, which can be changed from 0 to 1 but not back again. In a sequential setting, write-once memory (WOM) codes have been developed that allow simulating memory that support multiple writes, even of large values, setting an average of 1+o(1) write-once bits per write. We show that similar space efficiencies can be obtained in a concurrent setting, though at the cost of high time complexity and fixed bound on the number of write operations. As an alternative, we give an implementation that permits unboundedly many writes and has much better amortized time complexity, but at the cost of unbounded space complexity. Whether one can obtain both low time complexity and low space complexity in the same implementation remains open.