Parallel Communicating Grammar Systems As Language Analyzers

Abstract

Parallel communicating grammar systems 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 grammar systems with context-free productions. 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 generating case, and the language consists of all terminal words which can derive the axiom. We consider the usual variant and a restricted variant of accepting parallel communicating grammar systems and prove that all types of these accepting grammar systems characterize the family of recursively enumerable languages if the usual variant is considered, and that of context-free languages if the restricted one is used. The first result also holds 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 concept of generating derivation yielding to strong-returning parallel communicating grammar systems which also generate the family of recursively enumerable languages.