Grammar systems as language analyzers and recursively enumerable languages

Abstract

We consider parallel communicating grammar systems which consist of several grammars and perform derivation steps, where each of the grammars works in a parallel and synchronized manner on its own sentential form, and communication steps, where a transfer of sentential forms is done. We discuss accepting and analyzing versions of such gram- mar systems with context-free productions and present characterizations of the family of recursively enumerable languages by them. In accepting parallel communicating grammar systems rules of the form α → A with a word α and a nonterminal A are applied as in the gene- rating case, and the language consists of all terminal words which can derive the axiom. We prove that all types of these accepting grammar systems describe the family of recursively enumerable languages, even if λ-rules are forbidden. Moreover, we study analyzing parallel communicating grammar systems, the derivations of which perform the generating counterparts backwards. This requires a modification of the generating derivation concept to strong-returning parallel communicating grammar systems which also generate the family of recursively enumerable languages.