Formal Languages Questions
The main difference between a recursive language and a context-free language lies in the type of grammar used to generate them.
A recursive language is generated by a recursively enumerable grammar, also known as a type-0 grammar. This type of grammar allows for unrestricted rewriting rules and can generate any language that can be recognized by a Turing machine. Recursive languages are the most general class of languages and include both context-free and context-sensitive languages.
On the other hand, a context-free language is generated by a context-free grammar, which is a type-2 grammar. Context-free grammars have a more restricted form of rewriting rules, where the left-hand side of a rule consists of a single non-terminal symbol, and the right-hand side can be any combination of terminal and non-terminal symbols. Context-free languages can be recognized by pushdown automata, which are less powerful than Turing machines.
In summary, the main difference is that recursive languages are more general and can be generated by unrestricted grammars, while context-free languages have a more restricted form of grammar and can be recognized by pushdown automata.