I4ow I:o Reuse a "wri :e -once" Memoryt

Storage media such as digital optical disks, PROMS, or paper tape consist of a number of "write-once" bit positions (wigs); each wit initially contains a "0" that may later be irreversibly overwritten with a "1". We demonstrate 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 la.rge k, 1.29... • k wits sulllce to represent, a k-bit value in a way that can be simila.rly updated. Most surprising, allowing t writes of a k-bit value requires only t -qo(t) wits, for any fixed k. For fixed t, approximately k . t / log( t ) wits are required as k --~ oo. 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. " This research was supporte, I in part .L5" NSF grant MCS..8006938. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. © 1982 A C M O 8 9 7 9 1 0 6 7 2 / 8 2 / O 0 5 / O 1 0 5 $00.75