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:
“The conviction that the best way to prepare children for a harsh, rapidly changing world is to introduce formal instruction at an early age is wrong. There is simply no evidence to support it, and considerable evidence against it. Starting children early academically has not worked in the past and is not working now.”
—David Elkind (20th century)
“It is difficult for a woman to define her feelings in language which is chiefly made by men to express theirs.”
—Thomas Hardy (1840–1928)
“Frankly, these days, without a theory to go with it, I can’t see a painting.”
—Tom Wolfe (b. 1931)