Complexity and Application
Tree-adjoining grammars are often described as mildly context-sensitive, meaning that they possess certain properties that make them more powerful (in terms of weak generative capacity) than context-free grammars, but less powerful than indexed or context-sensitive grammars. Mildly context-sensitive grammars are conjectured to be powerful enough to model natural languages while remaining efficiently parsable in the general case.
A TAG can describe the language of squares (in which some arbitrary string is repeated), and the language . This type of processing can be represented by an embedded pushdown automaton.
Languages with cubes (i.e. triplicated strings) or with more than four distinct character strings of equal length cannot be generated by tree-adjoining grammars.
For these reasons, languages generated by tree-adjoining grammars are referred to as mildly context-sensitive languages.
Read more about this topic: Tree-adjoining Grammar
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