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:
“In the reproof of chance
Lies the true proof of men.”
—William Shakespeare (1564–1616)
“If we view our children as stupid, naughty, disturbed, or guilty of their misdeeds, they will learn to behold themselves as foolish, faulty, or shameful specimens of humanity. They will regard us as judges from whom they wish to hide, and they will interpret everything we say as further proof of their unworthiness. If we view them as innocent, or at least merely ignorant, they will gain understanding from their experiences, and they will continue to regard us as wise partners.”
—Polly Berrien Berends (20th century)
“What will happen once the authentic mass man takes over, we do not know yet, although it may be a fair guess that he will have more in common with the meticulous, calculated correctness of Himmler than with the hysterical fanaticism of Hitler, will more resemble the stubborn dullness of Molotov than the sensual vindictive cruelty of Stalin.”
—Hannah Arendt (1906–1975)