Abstract: A hardware virtualizer establishes correspondence between the real process names of the processes executing on a general purpose host computer and the virtual resource names of virtual resources simulated within a plurality of reserved areas of memory of the host computer as duplicates of the real resources, the virtualizer including: (1) a register for controlling access to the individual virtual operating levels; (2) a .phi.-map for selectively associating process names with real resource names at the real level of operation, termed the 0 level; (3) an f-map for establishing correspondence between the names of virtual resources being simulated at various levels of virtual operation, termed level (n+1) through n and successively higher levels to level 1; and (4) a composer mechanism for combining information accessed from the .phi.-map and the f-map for establishing correspondence between the virtual resource names and the real resource names.