Formal Languages Questions
The main difference between a pushdown automaton and a recursively enumerable grammar lies in their computational power and the way they generate languages.
A pushdown automaton (PDA) is a type of automaton that consists of a finite control, an input tape, and a stack. It can read symbols from the input tape, perform state transitions based on the current state and input symbol, and manipulate the stack. PDAs are capable of recognizing context-free languages, which are a subset of the recursively enumerable languages.
On the other hand, a recursively enumerable grammar (also known as a Type-0 grammar or unrestricted grammar) is a formal grammar that generates recursively enumerable languages. Recursively enumerable languages are a superset of context-free languages and include languages that can be recognized by Turing machines. Recursively enumerable grammars have more expressive power than PDAs as they can generate languages that are not context-free.
In summary, the main difference is that pushdown automata can recognize context-free languages, while recursively enumerable grammars can generate recursively enumerable languages, which are more powerful and include non-context-free languages.