As presented in Chapter 1, the generative power of eco-grammar systems was studied in several papers. In the original model of simple eco-grammar systems all the agents have to work in each derivation step, otherwise the derivation is blocked. In this section a different derivation mode is examined: in each derivation step exactly agents have to work.
First we summarise the results about the relation between language classes generated by simple eco-grammar systems with agents working in derivation mode . These results appeared in [Csuhaj-Varjú and KelemenováCsuhaj-Varjú and Kelemenová1998], and were summarised and completed in [CsimaCsima1997], where non-extended simple eco-grammar systems were studied.
The notion of extended simple eco-grammar systems was introduced in [Csuhaj-Varjú, Kelemen, Kelemenová, and PaunCsuhaj-Varjú et al.1997] and was examined first in [Dassow and MihalacheDassow and Mihalache1995] under the name of 0-terminal EG system. In the second part of the chapter we study the derivation mode in extended systems. The results, which appeared in [CsimaCsima1998a], show that unlike the non-extended case, where the size parameters of the teams and the agent population have influence on the power of the system, in the extended case a collapsing hierarchy is obtained.