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In formal language theory, a context-sensitive language is a formal language that can be defined by a context-sensitive grammar, where the applicability of a production rule may depend on the surrounding context of symbols. Unlike context-free grammars, which can apply rules regardless of context, context-sensitive grammars allow rules to be applied only when specific neighboring symbols are present, enabling them to express dependencies and agreements between distant parts of a string.
These languages correspond to type-1 languages in the Chomsky hierarchy and are equivalently defined by noncontracting grammars (grammars where production rules never decrease the total length of a string). Context-sensitive languages can model natural language phenomena such as subject-verb agreement, cross-serial dependencies, and other complex syntactic relationships that cannot be captured by simpler grammar types, making them important for computational linguistics and natural language processing.
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