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We study cooperating distributed grammar systems working in hybrid modes inconnection with the finite index restriction in two different ways: firstly, weinvestigate cooperating distributed grammar systems working in hybrid modeswhich characterize programmed grammars with the finite index restriction;looking at the number of components of such systems, we obtain surprisinglyrich lattice structures for the inclusion relations between the correspondinglanguage families. Secondly, we impose the finite index restriction oncooperating distributed grammar systems working in hybrid modes themselves,which leads us to new characterizations of programmed grammars of finite index.

Cooperating Distributed Grammar Systems of Finite Index Working in Hybrid Modes