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

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

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

Closure properties of bonded sequential insertion-deletion systems

Through the years, formal language theory has evolved through continual interdisciplinary work in theoretical computer science, discrete mathematics and molecular biology. The combination of these areas resulted in the birth of DNA computing. Here, language generating devices that usually considered any set of letters have taken on extra restrictions or modified constructs to simulate the behavior of recombinant DNA. A type of these devices is an insertion-deletion system, where the operations of insertion and deletion of a word have been combined in a single construct. Upon appending integers to both sides of the letters in a word, bonded insertion-deletion systems were introduced to accurately depict chemical bonds in chemical compounds. Previously, it has been shown that bonded sequential insertion-deletion systems could generate up to recursively enumerable languages. However, the closure properties of these systems have yet to be determined. In this paper, it is shown that bonded sequential insertion-deletion systems are closed under union, concatenation, concatenation closure, λ-free concatenation closure, substitution and intersection with regular languages. Hence, the family of languages generated by bonded sequential insertion-deletion systems is shown to be a full abstract family of languages

Combining Insertion and Deletion in RNA-editing Preserves Regularity

Inspired by RNA-editing as occurs in transcriptional processes in the living cell, we introduce an abstract notion of string adjustment, called guided rewriting. This formalism allows simultaneously inserting and deleting elements. We prove that guided rewriting preserves regularity: for every regular language its closure under guided rewriting is regular too. This contrasts an earlier abstraction of RNA-editing separating insertion and deletion for which it was proved that regularity is not preserved. The particular automaton construction here relies on an auxiliary notion of slice sequence which enables to sweep from left to right through a completed rewrite sequence.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347

Representations and characterizations of languages in Chomsky hierarchy by means of insertion-deletion systems

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schützenberger representation of context-free languages, i.e., in the form L = h(L( ) ∩D), where is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages – this time using insertion systems of weight (3, 0) and star languages.Ministerio de Educación y Ciencia TIN2006-1342