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.
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