Graph-Controlled Insertion-Deletion Systems

In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph: computational completeness can be obtained by systems with insertion or deletion rules involving at most two symbols in a contextual or in a context-free manner and with the control graph having only four nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127

DNA Hairpin Secondary Structure Design

In this thesis, we propose a bottom-up method to design single-stranded DNA sequences that form consecutive hairpin structures. This work was inspired by the hairpin-based DNA multi-state machine proposed by Takahashi et al. in 2004. They have successfully achieved this DNA multiple-hairpin structure in a laboratory experiment and proposed two possible applications. The first one is to construct a random access memory (RAM) by using the DNA machines as the access address for the data. The second one is to solve the maximum independent set problem (MISP). It is interesting thus to investigate how to design DNA sequences which form consecutive hairpin structures as mentioned above. We propose a bottom-up approach to construct consecutive hairpin structures, grounded on a so-called bond-free property, and several combinatorial constraints. A software is implemented to study the behavior of our bottom-up approach. We also calculate the maximal number of sequences that correctly fold into the desired multiple-hairpin structure. This calculation provides an estimation for the size of the memory that can be constructed using Takahashi et aVs method. Lastly, by selecting suitable parameters, we successfully construct a set of sequences that can fold in to the desirable multiple-hairpin structure. For example, our software is able to generate 120 sequences that can fold into a four-hairpin structure where the length of each hairpin stem is 20, the length of each hairpin loop is 7 and the external segment is 20. We validate these sequences using the molecule secondary structure prediction package, Vienna RNA secondary structure package

Complexity and modeling power of insertion-deletion systems

SISTEMAS DE INSERCIÓN Y BORRADO: COMPLEJIDAD Y CAPACIDAD DE MODELADO El objetivo central de la tesis es el estudio de los sistemas de inserción y borrado y su capacidad computacional. Más concretamente, estudiamos algunos modelos de generación de lenguaje que usan operaciones de reescritura de dos cadenas. También consideramos una variante distribuida de los sistemas de inserción y borrado en el sentido de que las reglas se separan entre un número finito de nodos de un grafo. Estos sistemas se denominan sistemas controlados mediante grafo, y aparecen en muchas áreas de la Informática, jugando un papel muy importante en los lenguajes formales, la lingüística y la bio-informática. Estudiamos la decidibilidad/ universalidad de nuestros modelos mediante la variación de los parámetros de tamaño del vector. Concretamente, damos respuesta a la cuestión más importante concerniente a la expresividad de la capacidad computacional: si nuestro modelo es equivalente a una máquina de Turing o no. Abordamos sistemáticamente las cuestiones sobre los tamaños mínimos de los sistemas con y sin control de grafo.COMPLEXITY AND MODELING POWER OF INSERTION-DELETION SYSTEMS The central object of the thesis are insertion-deletion systems and their computational power. More specifically, we study language generating models that use two string rewriting operations: contextual insertion and contextual deletion, and their extensions. We also consider a distributed variant of insertion-deletion systems in the sense that rules are separated among a finite number of nodes of a graph. Such systems are refereed as graph-controlled systems. These systems appear in many areas of Computer Science and they play an important role in formal languages, linguistics, and bio-informatics. We vary the parameters of the vector of size of insertion-deletion systems and we study decidability/universality of obtained models. More precisely, we answer the most important questions regarding the expressiveness of the computational model: whether our model is Turing equivalent or not. We systematically approach the questions about the minimal sizes of the insertiondeletion systems with and without the graph-control

Combinatorial Aspects of Minimal DNA Expressions

Algorithms and the Foundations of Software technolog