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:
“I will not let him stir
Till I have used the approvèd means I have,
With wholesome syrups, drugs, and holy prayers,
To make of him a formal man again.”
—William Shakespeare (1564–1616)
“Men sometimes speak as if the study of the classics would at length make way for more modern and practical studies; but the adventurous student will always study classics, in whatever language they may be written and however ancient they may be. For what are the classics but the noblest recorded thoughts of man?... We might as well omit to study Nature because she is old.”
—Henry David Thoreau (1817–1862)
“Every theory is a self-fulfilling prophecy that orders experience into the framework it provides.”
—Ruth Hubbard (b. 1924)