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A hierarchy of language families. If two families are connected by a line (an arrow), the upper family includes (includes properly) the lower family. If two families are not connected, they are not necessarily incomparable.
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In this paper, we discuss cooperating distributed grammar systems where components are (variants of) random context grammars. We give an overview of known results and open problems, and prove some further results.
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Citations
... In view of these results, the results of the present paper are of some interest because the cooperation increases the generative power of cooperating distributed grammar systems with left-forbidding components from the power of context-free grammars to the power of context sensitive or phrase structure grammars. On the other hand, however, this increase does not hold for cooperating distributed grammar systems with random context components because they are as powerful as random context grammars (see [9, 10]). Consequently, although random context grammars are more powerful than left-forbidding grammars, cooperating random context grammars are not as powerful as cooperating left-forbidding grammars. ...
A left-forbidding grammar, introduced in this paper, is a context-free grammar, where a set of nonterminal symbols is attached to each context-free production. Such a production can rewrite a nonterminal provided that no symbol from the attached set occurs to the left of the rewritten nonterminal in the current sentential form. The present paper discusses cooperating distributed grammar systems with left-forbidding grammars as components and gives some new characterizations of language families of the Chomsky hierarchy. In addition, it also proves that twelve nonterminals are enough for cooperating distributed grammar systems working in the terminal derivation mode with two left-forbidding components (including erasing productions) to characterize the family of recursively enumerable languages.
This three-section chapter makes several final remarks concerning the material covered in this book. First, Sect.21.1 describes new investigation trends closely related to regulated grammars and automata. Second, Sect. 21.2 suggests several open problem areas to the future study concerning the subject of this book. Finally, Sect.21.3 gives an overview of significant studies published on the subject of this book from a historical perspective. This chapter contains an unusually great number of references in order to demonstrate the significance of all its coverage in a specific and detailed way.
