Formal Languages Questions
The main difference between a regular language and a recursively enumerable grammar lies in their expressive power and the type of languages they can generate.
A regular language is a language that can be recognized by a finite-state automaton, such as a deterministic finite automaton (DFA) or a non-deterministic finite automaton (NFA). Regular languages are characterized by their ability to be described using regular expressions or generated by regular grammars. They are limited in their expressive power and can only represent simple patterns and regular structures.
On the other hand, a recursively enumerable grammar, also known as a type-0 grammar or unrestricted grammar, is a more powerful formalism that can generate any language that can be recognized by a Turing machine. Recursively enumerable grammars have no restrictions on the production rules or the form of the grammar, allowing for more complex and arbitrary language structures to be generated. They can describe languages that are not regular, such as context-sensitive or context-free languages.
In summary, the key difference is that regular languages are limited in their expressive power and can be recognized by finite-state automata, while recursively enumerable grammars have no restrictions and can generate any language recognized by a Turing machine.