a "page allocation table" (pat) maps the logical pages to the physical pages. each pat is just a physical page located at well-defined locations. like the fcrs, pats always occur in pairs, with the currently valid copy indicated by having a higher usage count. the first pair of pats immediately follow the first two fcrs and takes up physical pages 2 and 3. a variable number of other pages follow, and a new pair of pats in turn follow this. each pat has a fixed number of pointers to logical pages, with each entry that is empty having a value of zero.