Formal Languages Questions Medium
The main difference between a context-free language and a recursively enumerable language lies in the level of complexity and generative power.
A context-free language is a type of formal language that can be generated by a context-free grammar. It is characterized by the fact that its production rules only allow for the replacement of a single non-terminal symbol with a sequence of terminal and/or non-terminal symbols. Context-free languages can be recognized by pushdown automata, which have a stack memory to keep track of the non-terminal symbols.
On the other hand, a recursively enumerable language is a more general type of formal language that can be recognized by a Turing machine. It is characterized by the fact that there exists a Turing machine that, given an input string, will eventually halt and accept if the string belongs to the language, but may either halt and reject or loop indefinitely if the string does not belong to the language. Recursively enumerable languages can be generated by unrestricted grammars, which have more powerful production rules that allow for arbitrary replacements.
In summary, the key difference is that context-free languages can be generated by context-free grammars and recognized by pushdown automata, while recursively enumerable languages can be recognized by Turing machines and generated by unrestricted grammars. Recursively enumerable languages have a higher level of complexity and generative power compared to context-free languages.