Bit Vector Representations
Subsets of a finite set can be efficiently represented as bit vectors, in which a given bit position is a 1 if the corresponding item is an element of the subset. Representing a 128-element set takes only 4 32-bit words of memory.
Operations on sets can be done by boolean instructions operating on whole words.
| Set operation: | Bit vector operation: |
| &isin | &and with vector for element |
| or test bit | |
| &cap | &and |
| &cup | &or |
| set complement of A | ¬ A |
| set difference, A - B | A &and ¬ B |
Operations on the bit vector representation are O(n/32) , compared to O(n · m) with other methods.
Example use: assign a bit in a bit vector for each program variable or subexpression.