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:
“On every formal visit a child ought to be of the party, by way of provision for discourse.”
—Jane Austen (1775–1817)
“Experiment is necessary in establishing an academy, but certain principles must apply to this business of art as to any other business which affects the artis tic sense of the community. Great art speaks a language which every intelligent person can understand. The people who call themselves modernists today speak a different language.”
—Robert Menzies (1894–1978)
“By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.”
—Abraham Lincoln (1809–1865)