Automata Theory Questions Medium
A context-sensitive grammar is a formal grammar that consists of a set of production rules, where each rule has the form α → β, where α and β are strings of symbols. The key characteristic of a context-sensitive grammar is that it allows for the rewriting of symbols in a context-dependent manner, meaning that the replacement of symbols is based on the surrounding context or the neighboring symbols.
In a context-sensitive grammar, the left-hand side of a production rule can be any non-empty string of symbols, and the right-hand side can be any string of symbols, as long as the length of the right-hand side is greater than or equal to the length of the left-hand side. This restriction ensures that the grammar can rewrite symbols in a context-dependent manner.
Context-sensitive grammars are more powerful than regular grammars and context-free grammars, as they can generate languages that cannot be generated by these weaker types of grammars. They are often used in the study of formal languages and automata theory to describe natural languages, programming languages, and other complex systems.