Formal Languages Questions
The main difference between a recursively enumerable language and a context-sensitive language lies in the restrictions imposed on the rules and structures of the languages.
A recursively enumerable language is a type of formal language that can be recognized by a Turing machine. It means that there exists a Turing machine that, when given an input string belonging to the language, will eventually halt and accept the string. However, if the input string does not belong to the language, the Turing machine may either halt and reject the string or run indefinitely.
On the other hand, a context-sensitive language is a type of formal language that can be generated by a context-sensitive grammar. In this case, the rules for generating the language are more restricted compared to recursively enumerable languages. A context-sensitive grammar allows for rules where the left-hand side can be replaced by the right-hand side, but the length of the left-hand side must be less than or equal to the length of the right-hand side. This restriction ensures that the language can be recognized by a linear-bounded automaton, which is a more limited computational model compared to a Turing machine.
In summary, the main difference is that recursively enumerable languages can be recognized by Turing machines, while context-sensitive languages can be generated by context-sensitive grammars and recognized by linear-bounded automata.