This paper investigates the reduction of scattered context grammars with respect to the number of non-context-free productions. It proves that every recursively enumerable language is generated by a scattered context grammar that has no more than one non-context-free production. An open problem is formulated.

This paper introduces and studies jumping pure grammars, which are conceptualized just like classical pure grammars except that during the applications of their productions, they can jump over symbols in either direction within the rewritten strings. The paper compares the generative power of jumping pure grammars with that of classical pure grammars while distinguishing between their versions with and without erasing productions. Apart from sequential versions, the paper makes an analogical study in terms of parallel versions of jumping pure grammars represented by 0L grammars.

This paper establishes two new normal forms for phrase-structure grammars in which both context-free rules and non-context-free rules are in prescribed forms. In addition, a limit is placed on the number of context-free rules. More specifically, the first form has | $2 + n$ | context-free rules, where | $n$ | is the number of terminals. Concerning non-context-free rules, each of them has the form | $AB \rightarrow CD$ | , where | $A, B, C, D$ | are nonterminals. The second normal form has always only two context-free rules— | $S \to S\#$ | and | $\# \to \varepsilon $ | , where | $S$ | is the start symbol, | $\#$ | is a nonterminal, and | $ \varepsilon $ | is the empty string. Regarding non-context-free rules, each of them is of the form | $AB \rightarrow XD$ | , where | $A, B, D$ | are nonterminals and | $X$ | is a nonterminal or a terminal.