Formal Languages Questions
The main difference between a context-free language and a context-sensitive grammar lies in their respective levels of generative power and the restrictions they impose on the rules of a formal language.
A context-free language is a type of formal language that can be generated by a context-free grammar. In a context-free grammar, the left-hand side of each production rule consists of a single non-terminal symbol, and the right-hand side can be any combination of terminal and non-terminal symbols. The rules in a context-free grammar do not depend on the context or surrounding symbols, hence the name "context-free." Context-free languages are less powerful than context-sensitive languages.
On the other hand, a context-sensitive grammar is a type of formal grammar that generates a context-sensitive language. In a context-sensitive grammar, the left-hand side of each production rule can consist of multiple symbols, including both terminal and non-terminal symbols. The right-hand side of the rule can also be any combination of symbols, but it must be at least as long as the left-hand side. The rules in a context-sensitive grammar can depend on the context or surrounding symbols, allowing for more flexibility in generating languages. Context-sensitive languages are more powerful than context-free languages.
In summary, the key difference between a context-free language and a context-sensitive grammar is the level of generative power and the restrictions imposed on the rules. Context-free languages can be generated by context-free grammars, while context-sensitive languages require context-sensitive grammars.