k-Limited Erasing Performed by Scattered Context Grammars

A scattered context grammar, G, erases nonterminals in a k-limited way, where k≥ 1, if in every sentential form of any derivation, between every two symbols from which G derives non-empty strings, there occur no more than k nonterminals from which G derives empty words. This paper demonstrates that any scattered context grammar that erases nonterminals in this way can be converted to an equivalent scattered context grammar without any erasing productions while in general, this conversion is impossible.