Abstract

Well investigated are growing context-sensitive languages (GCSL), i. e. languages defined by grammars that have only growing rules, where the left side of a growing rule is shorter than its right side. GCSL is characterized by quasi growing context-sensitive grammars (QGCSG), i. e. the rules therein are growing only with respect to a valuation of all the strings by a homomorphism to natural numbers with addition. In this paper we introduce weak growing context-sensitive grammars (WGCSG), i. e. grammars that are growing with a weighted valuation of all strings, where the weights are the values of a position valuation. Here we evaluate a string by summing up every product of a symbol value with its position value. For every position valuation which does not agree with the beginning of any exponential function, the corresponding class of WGCSGs characterizes CSL, shown by a somehow tricky proof. Such a valuation function is called unsteady. On the other hand all WGCSG related to steady ...

Citations