On the number of components for some parallel communicating grammar systems

In natural languages, there occur phenomena like multiple agreements, crossed agreements and replication. These aspects are represented by the three languages , and , respectively. These languages are of interest, when modeling natural languages.In the present paper, we give parallel communicating grammar systems (PC grammar systems) that generate the languages K1, K2 and K3 but use less or less-powerful components than those used by systems published so far.