Formal Languages Questions Medium
The main difference between a context-sensitive language and a recursively enumerable language lies in the restrictions imposed on the rules and structures of 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 language, the rules for generating strings are more flexible compared to other types of formal languages. The rules allow for the manipulation of symbols based on the context in which they appear. Specifically, the left-hand side of the production rule can be replaced by the right-hand side, but the context surrounding the symbols must be preserved. Context-sensitive languages are more expressive than regular languages and context-free languages.
On the other hand, a recursively enumerable language is a type of formal language that can be recognized by a Turing machine. In this type of language, there are no restrictions on the rules or structures of the language. A Turing machine can accept or reject any string in the language, but it may not halt for strings that are not in the language. This means that a recursively enumerable language can have undecidable problems, where the Turing machine may run indefinitely without reaching a conclusion.
In summary, the main difference between a context-sensitive language and a recursively enumerable language is that context-sensitive languages have more restricted rules and structures, while recursively enumerable languages have no restrictions and can have undecidable problems.