Recursively enumerable languages are not closed under set difference or complementation.
2.
It may be shown that unrestricted grammars characterize the recursively enumerable languages.
3.
Let L be a recursively enumerable language.
4.
Recursively enumerable languages are intersection, but not under set difference; see Recursively enumerable language # Closure properties.
5.
Recursively enumerable languages are intersection, but not under set difference; see Recursively enumerable language # Closure properties.
6.
A universal Turing machine can calculate any recursive function, decide any recursive language, and accept any recursively enumerable language.
7.
A language which is accepted by such a Turing machine is called a "'recursively enumerable language " '.
8.
Recursively enumerable languages are known as "'type-0 "'languages in the Chomsky hierarchy of formal languages.
9.
Within the Chomsky hierarchy, the regular languages, the context-free languages, and the recursively enumerable languages are all full AFLs.
10.
Such sets are recursively enumerable languages and every recursively enumerable language is the restriction of some such set to a sub-alphabet of "'A " '.
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