Proof of Correctness
The binary operation XOR over bit strings of length exhibits the following properties (where denotes XOR):
- L1. Commutativity:
- L2. Associativity:
- L3. Identity exists: there is a bit string, 0, (of length N) such that for any
- L4. Each element is its own inverse: for each, .
Suppose that we have two distinct registers R1 and R2 as in the table below, with initial values A and B respectively. We perform the operations below in sequence, and reduce our results using the properties listed above.
| Step | Operation | Register 1 | Register 2 | Reduction |
|---|---|---|---|---|
| 0 | Initial value | — | ||
| 1 | R1 := R1 XOR R2 |
— | ||
| 2 | R2 := R1 XOR R2 |
L2 L4 L3 |
||
| 3 | R1 := R1 XOR R2 |
L1 L2 L4 L3 |
Read more about this topic: XOR Swap Algorithm
Famous quotes containing the words proof of, proof and/or correctness:
“The fact that several men were able to become infatuated with that latrine is truly the proof of the decline of the men of this century.”
—Charles Baudelaire (1821–1867)
“a meek humble Man of modest sense,
Who preaching peace does practice continence;
Whose pious life’s a proof he does believe,
Mysterious truths, which no Man can conceive.”
—John Wilmot, 2d Earl Of Rochester (1647–1680)
“The surest guide to the correctness of the path that women take is joy in the struggle. Revolution is the festival of the oppressed.”
—Germaine Greer (b. 1939)