Cooperating Distributed Grammar Systems of Finite Index Working in Hybrid Modes

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.Comment: In Proceedings AFL 2014, arXiv:1405.527

Petri net controlled grammars

Different types of regulated grammars have been introduced in order to supplement shortcomings of context-free grammars in applications preserving their elegant mathematical properties. However, the rapid developments in present day industry, biology, and other areas challenge to deal with various tasks which need suitable tools for their modelling and investigation. We propose Petri net controlled grammars as models for representing and analyzing of metabolic pathways in living cells where Petri nets are responsible for the structure and communication of the pathways, and grammars represent biochemical processes. On the other hand, the control by Petri nets has also theoretical interest: it extends possibilities to introduce and investigate concurrent control mechanisms in formal language theory. The thesis introduces various variants of Petri net controlled grammars using different types of Petri nets and investigates their mathematical properties such as computational power and closure properties.Los diferentes tipos de gramáticas con reescritura regulada han sido introducidas para complementar las deficiencias de las gramáticas libres del contexto en las aplicaciones, preservando sus propiedades matemáticas. Por otro lado, la rápida evolución la biología, y otras áreas actuales supone un reto para tratar de las tareas varias que necesitan las herramientas adecuadas para la elaboración de modelos e investigación. Proponemos gramáticas controladas por redes de Petri como modelos para representar y analizar los procesos bioquímicos en las células vivas donde redes de Petri son responsables de la estructura, y gramáticas representan los procesos generativos. Además, el control de redes de Petri también tiene interés teórico: amplía las posibilidades de investigar los mecanismos de control concurrente en la teoría de lenguajes formales. La tesis presenta distintas variantes de gramáticas controladas por redes de Petri e investiga sus propiedades matemáticas