How to Reuse a "Write-Once" Memory

Storage media such as digital optical disks, PROMS, or paper tape consist of a number of "write-once" bit positions (wits); each wit initially contains a "0" that may later be irreversibly overwritten with a "1." It is demonstrated that such "write-once memories" (woms) can be "rewritten" to a surprising degree. For example, only 3 wits suffice to represent any 2-bit value in a way that can later be updated to represent any other 2-bit value. For large k, 1.29.... k wits suffice to represent a k-bit value in a way that can be similarly updated. Most surprising, allowing t writes of a k-bit value requires only t + o(t) wits, for any fixed k. For fixed t, approximately k. t/log(t) wits are required as k~ c~. An n-wit WOM is shown to have a "capacity" (i.e., k • t when writing a k-bit value l times) of up to n • log(n) bits.