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:
“I could buy one
Tape and get another free. I accept- Ed the deal, paid for one tape and
Chose a free one. But since I’ve been
Repeatedly billed for my free tape.”
—John Ashbery (b. 1927)