Homomorphisms and E-free Homomorphisms in Formal Language Theory
Homomorphisms are also used in the study of formal languages (although within this context, often they are briefly referred to as morphisms). Given alphabets and, a function h : → such that for all u and v in is called a homomorphism (or simply morphism) on . Let e denote the empty word. If h is a homomorphism on and for all in, then h is called an e-free homomorphism.
This type of homomorphism can be thought of as (and is equivalent to) a monoid homomorphism where the set of all words over a finite alphabet is a monoid (in fact it is the free monoid on ) with operation concatenation and the empty word as the identity.
Read more about this topic: Homomorphism
Famous quotes containing the words formal, language and/or theory:
“Then the justice,
In fair round belly with good capon lined,
With eyes severe and beard of formal cut,
Full of wise saws and modern instances;
And so he plays his part.”
—William Shakespeare (1564–1616)
“The language of Friendship is not words, but meanings. It is an intelligence above language.”
—Henry David Thoreau (1817–1862)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)