Formal Languages Questions Medium
A recursively enumerable grammar, also known as a Type-0 grammar or unrestricted grammar, is a formal grammar that generates a recursively enumerable language.
In formal language theory, a grammar is a set of production rules that define the structure of a language. A recursively enumerable grammar is the most general type of grammar, allowing for the generation of any language that can be recognized by a Turing machine.
A language is considered recursively enumerable if there exists a Turing machine that can enumerate (list) all the strings in that language. Similarly, a grammar is recursively enumerable if there exists a Turing machine that can generate (list) all the strings that can be derived from the grammar.
In a recursively enumerable grammar, there are no restrictions on the production rules or the derivation process. This means that the grammar can have non-context-free rules, non-terminating derivations, or even rules that produce infinite strings. The generative power of a recursively enumerable grammar is equivalent to that of a Turing machine, making it the most powerful type of grammar in terms of language recognition.
Overall, a recursively enumerable grammar is a formal grammar that can generate any language that can be recognized by a Turing machine, allowing for the generation of complex and unrestricted languages.