Formal Languages Questions
The difference between a context-free language and a recursively enumerable grammar lies in their respective definitions and properties.
A context-free language is a type of formal language that can be generated by a context-free grammar. A context-free grammar consists of a set of production rules that define how symbols can be combined to form strings in the language. The language generated by a context-free grammar can be recognized by a non-deterministic pushdown automaton.
On the other hand, a recursively enumerable grammar, also known as a type-0 grammar, is a more general type of formal grammar. It can generate languages that are not necessarily context-free. A recursively enumerable grammar consists of a set of production rules that define how symbols can be combined to form strings in the language. The language generated by a recursively enumerable grammar can be recognized by a Turing machine.
In summary, the main difference is that a context-free language can be generated by a context-free grammar and recognized by a non-deterministic pushdown automaton, while a recursively enumerable grammar can generate languages that are not necessarily context-free and can be recognized by a Turing machine.