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:
“There are some who praise a man free from disease; to me no man who is poor seems free from disease but to be constantly sick.”
—Sophocles (497–406/5 B.C.)