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 → ∞. An n-wit WOM is shown to have a “capacity≓ (i.e., k · t when writing a k -bit value t times) of up to n · log( n ) bits.