95 research outputs found
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
Membrane Computing Schema: A New Approach to Computation Using String Insertions
In this paper, we introduce the notion of a membrane computing schema
for string objects. We propose a computing schema for a membrane network (i.e.,
tissue-like membrane system) where each membrane performs unique type of operations
at a time and sends the result to others connected through the channel. The
distinguished features of the computing models obtained from the schema are:
1. only context-free insertion operations are used for string generation,
2. some membranes assume filtering functions for structured objects (molecules),
3. generating model and accepting model are obtained in the same schema, and
both are computationally universal,
4. several known rewriting systems with universal computability can be reformulated
by the membrane computing schema in a uniform manner.
The first feature provides the model with a simple uniform structure which facilitates
a biological implementation of the model, while the second feature suggests further
feasibility of the model in terms of DNA complementarity.
Through the third and fourth features, one may have a unified view of a variety of
existing rewriting systems with Turing computability in the framework of membrane
computing paradigm.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58
On the Power of Insertion P Systems of Small Size
In this article we investigate insertion systems of small size in the framework
of P systems. We consider P systems with insertion rules having one symbol context and
we show that they have the computational power of matrix grammars. If contexts of
length two are permitted, then any recursively enumerable language can be generated.
In both cases an inverse morphism and a weak coding were applied to the output of the
corresponding P systems
P Systems with Minimal Insertion and Deletion
In this paper we consider insertion-deletion P systems with priority of deletion over the insertion.We show that such systems with one symbol context-free insertion
and deletion rules are able to generate PsRE. If one-symbol one-sided context is added
to insertion or deletion rules but no priority is considered, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is
permitted. We also show that the priority relation is very important and in its absence
the corresponding class of P systems is strictly included in MAT
On the Power of Small Size Insertion P Systems
In this article we investigate insertion systems of small size in the framework of P systems. We consider P systems with insertion rules having one symbol context and we show that they have the computational power of context-free matrix grammars. If contexts of length two are permitted, then any recursively enumerable language can be generated. In both cases a squeezing mechanism, an inverse morphism, and a weak coding are applied to the output of the corresponding P systems. We also show that if no membranes are used then corresponding family is equal to the family of context-free languages
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
Formal models of the extension activity of DNA polymerase enzymes
The study of formal language operations inspired by enzymatic actions on DNA is part of ongoing efforts to provide a formal framework and rigorous treatment of DNA-based information and DNA-based computation. Other studies along these lines include theoretical explorations of splicing systems, insertion-deletion systems, substitution, hairpin extension, hairpin reduction, superposition, overlapping concatenation, conditional concatenation, contextual intra- and intermolecular recombinations, as well as template-guided recombination.
First, a formal language operation is proposed and investigated, inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called the primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called the template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L1 and a primer language L2. This language operation is called L1-directed extension of L2 and the closure properties of various language classes, including the classes in the Chomsky hierarchy, are studied under directed extension. Furthermore, the question of finding necessary and sufficient conditions for a given language of target strings to be generated from a given template language when the primer language is unknown is answered. The canonic inverse of directed extension is used in order to obtain the optimal solution (the minimal primer language) to this question.
The second research project investigates properties of the binary string and language operation overlap assembly as defined by Csuhaj-Varju, Petre and Vaszil as a formal model of the linear self-assembly of DNA strands: The overlap assembly of two strings, xy and yz, which share an overlap y, results in the string xyz. In this context, we investigate overlap assembly and its properties: closure properties of various language families under this operation, and related decision problems. A theoretical analysis of the possible use of iterated overlap assembly to generate combinatorial DNA libraries is also given.
The third research project continues the exploration of the properties of the overlap assembly operation by investigating closure properties of various language classes under iterated overlap assembly, and the decidability of the completeness of a language. The problem of deciding whether a given string is terminal with respect to a language, and the problem of deciding if a given language can be generated by an overlap assembly operation of two other given languages are also investigated
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