How to reuse a "write - once " memory (Preliminary Version)

Abstract

Storage media such as digital optical disks, PROMS, or paper tape consist of a number of -&-ldquo;write-once-&-rdquo; bit positions (wits); each wit initially contains a -&-ldquo;0-&-rdquo; that may later be irreversibly overwritten with a -&-ldquo;I-&-rdquo;. We demonstrate that such -&-ldquo;write-once memories-&-rdquo; (woms) can be -&-ldquo;rewritten-&-rdquo; 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 -&-rarr;