Formal Languages Questions
The main difference between a context-sensitive language and a recursively enumerable language lies in the restrictions imposed on the rules or productions that generate the languages.
A context-sensitive language is a type of formal language that can be generated by a context-sensitive grammar. In this type of grammar, the rules or productions are of the form α → β, where α and β are strings of symbols, and the length of α is less than or equal to the length of β. The context-sensitive languages can be recognized by a linear bounded automaton, which is a non-deterministic Turing machine with a tape that can only move within a limited portion of the input.
On the other hand, a recursively enumerable language is a type of formal language that can be generated by a recursively enumerable grammar. In this type of grammar, the rules or productions have no restrictions on the lengths of α and β. The recursively enumerable languages can be recognized by a Turing machine, which is a computational device that can simulate any other computational device.
In summary, the main difference is that context-sensitive languages have restrictions on the lengths of the rules or productions, while recursively enumerable languages have no such restrictions. Additionally, context-sensitive languages can be recognized by a linear bounded automaton, whereas recursively enumerable languages can be recognized by a Turing machine.