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:
“The majority is never right. Never, I tell you! That’s one of these lies in society that no free and intelligent man can help rebelling against. Who are the people that make up the biggest proportion of the population—the intelligent ones or the fools? I think we can agree it’s the fools, no matter where you go in this world, it’s the fools that form the overwhelming majority.”
—Henrik Ibsen (1828–1906)