1. A method operable within an optimizing compiler for generating Basis items and Kill Sets for use during subsequent global common subexpression elimination and code motion procedures, said method comprising: creating a tuple (v) for each computation which is to be converted to a machine instruction by the compiler, creating a table having an entry for all the tuples in the program being compiled, assigning a symbolic register to each tuple created, for every Basis item in a tuple being entered in the table adding to the Kill Set for that Basis item, a symbolic register uniquely assigned to that tuple, for every non-basis item "n" in the tuple being entered into the table, adding the uniquely assigned symbolic register for that tuple to the Kill Sets for all the Basis items in whose Kill Sets that non-basis item "n" appears, designating the symbolic register assigned to the tuple in the table to the result of the computation of the non-basis element, and constructing a second table of assigned symbolic registers whereby the computation to which each symbolic register has been assigned can be readily retrieved.