Formal Languages Questions Medium
A context-sensitive grammar is a formal grammar that consists of a set of production rules used to generate strings in a formal language. It is a type of formal grammar that allows for rules to be applied based on the context or surrounding symbols of a given symbol in a string. In other words, the production rules of a context-sensitive grammar are more flexible than those of a context-free grammar, as they can take into account the context in which a symbol appears.
Formally, a context-sensitive grammar is defined as a 4-tuple (V, Σ, P, S), where:
- V is a finite set of variables or non-terminals.
- Σ is a finite set of terminals.
- P is a finite set of production rules of the form α → β, where α and β are strings of variables and terminals, and the length of α is less than or equal to the length of β.
- S is the start symbol, which is a special variable in V.
The production rules of a context-sensitive grammar can be applied to transform a given string by replacing a substring that matches the left-hand side of a production rule with the corresponding right-hand side. However, the application of these rules is subject to the condition that the context or surrounding symbols of the substring being replaced must satisfy certain constraints specified by the grammar.
Context-sensitive grammars are more powerful than context-free grammars, as they can generate languages that cannot be generated by context-free grammars. They are often used in the study of natural language processing, programming languages, and formal language theory.