A note on cooperating distributed grammar systems working in combined modes

We investigate the generative power of cooperating distributed grammar systems with context-free rules working in the full-competence mode in combination with another derivation mode, combined sf-mode, for short. A combined sf-mode as, for example, (sf∧⩽k) restricts the valid derivations such that both properties have to be satisfied. If erasing rules are allowed, then except for the (sf∧⩽1)-, (sf∧=1)-, and (sf∧t)-modes, it is shown that the family of recursively enumerable languages is characterized. The former two exceptions characterize the family of linear context-free languages, while the latter mode describes the family of context-free languages.