The contextsensitivity bounds of contextsensitive grammars and languages
In this paper we study the derivational complexity of contextsensitive grammars and languages by placing bounds on their contextsensitivity. The contextsensitivity of a grammar is defined on its derivations, and it is determined by the maximal length of the strings of ancestors of any symbol occurring at any position of the derived strings. A total recursive function f bounds the (right-) contextsensitivity function of grammar G, if for every terminal string x of length n generated by G there is a (right-canonical) derivation from S to x in G whose contextsensitivity is less than or equal to f(n).
We investigate lower and upper bounding functions for the right-contextsensitivity functions of contextsensitive grammars and languages and study the families of context-sensitive languages with right-contextsensitivity functions bounded by some particular sublinear functions f.
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