Free Hull
The intersection of free submonoids of a free monoid A∗ is again free. If S is a subset of a free monoid A* then the intersection of all free submonoids of A* containing S is well-defined, since A* itself is free, and contains S; it is a free monoid. A basis for this intersection is the free hull of S.
The defect theorem states that if X is finite and C is the free hull of X, then either X is a code and C = X, or
- |C| ≤ |X| − 1 .
Read more about this topic: Free Monoid
Famous quotes containing the word free:
“It may be that the most interesting American struggle is the struggle to set oneself free from the limits one is born to, and then to learn something of the value of those limits.”
—Greil Marcus (b. 1945)