Two power-decreasing derivation restrictions in generalized scattered context grammars

Abstract

The present paper introduces and discusses generalized scattered context grammars that are based upon sequences of productions whose left-hand sides are formed by nonterminal strings, not just single nonterminals. It places two restrictions on the derivations in these grammars. More specifically, let k be a positive integer. The first restriction requires that all rewritten symbols occur within the first k symbols of the first continuous block of nonterminals in the sentential form during every derivation step. The other restriction defines derivations over sentential forms containing no more than k occurrences of nonterminals. As its main result, the paper demonstrates that both restrictions decrease the generative power of these grammars to the power of context-free grammars.