Control Language Hierarchy
A more precisely defined hierarchy of languages that correspond to the mildly context-sensitive class was defined by David J. Weir. Based on the work of Nabil A. Khabbaz, Weir's Control Language Hierarchy is a containment hierarchy of countable set of language classes where the Level-1 is defined as context-free, and Level-2 is the class of tree-adjoining and the other three grammars.
Following are some of the properties of Level-k languages in the hierarchy:
- Level-k languages are properly contained in the Level-(k + 1) language class
- Level-k languages can be parsed in time
- Level-k contains the language, but not
- Level-k contains the language, but not
Those properties correspond well (at least for small k > 1) to the conditions of mildly context-sensitive languages imposed by Joshi, and as k gets bigger, the language class becomes, in a sense, less mildly context-sensitive.
Read more about this topic: Mildly Context-sensitive Language
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