Cooperating Distributed Grammar Systems of Finite Index Working in Hybrid Modes

TL;DR

This paper explores how cooperating distributed grammar systems operating in hybrid modes relate to finite index restrictions, revealing complex lattice structures and new characterizations of programmed grammars with finite index.

Contribution

It introduces novel connections between hybrid mode grammar systems and finite index restrictions, providing new insights and characterizations in formal language theory.

Findings

Rich lattice structures for language family inclusions

New characterizations of programmed grammars with finite index

Connections between hybrid mode systems and finite index restrictions

Abstract

We study cooperating distributed grammar systems working in hybrid modes in connection with the finite index restriction in two different ways: firstly, we investigate cooperating distributed grammar systems working in hybrid modes which characterize programmed grammars with the finite index restriction; looking at the number of components of such systems, we obtain surprisingly rich lattice structures for the inclusion relations between the corresponding language families. Secondly, we impose the finite index restriction on cooperating distributed grammar systems working in hybrid modes themselves, which leads us to new characterizations of programmed grammars of finite index.