72 research outputs found
Regulated Formal Models and Their Reduction
Department of Theoretical Computer Science and Mathematical LogicKatedra teoretické informatiky a matematické logikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
P Systems with Minimal Left and Right Insertion and Deletion
In this article we investigate the operations of insertion and deletion performed
at the ends of a string. We show that using these operations in a P systems
framework (which corresponds to using specific variants of graph control), computational
completeness can even be achieved with the operations of left and right insertion and
deletion of only one symbol
Simple-Semi-Conditional Versions of Matrix Grammars with a Reduced Regulating Mechanism
This paper discusses some conditional versions of matrix grammars. It establishes several characterizations of the family of the recursively enumerable languages based on these grammars. In fact, making use of the Geffert Normal forms, the present paper demonstrates these characterizations based on matrix grammars with conditions of a limited length, a reduced number of nonterminals, and a reduced number and size of matrices
Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability
Previously referred to as `miraculous' in the scientific literature because
of its powerful properties and its wide application as optimal solution to the
problem of induction/inference, (approximations to) Algorithmic Probability
(AP) and the associated Universal Distribution are (or should be) of the
greatest importance in science. Here we investigate the emergence, the rates of
emergence and convergence, and the Coding-theorem like behaviour of AP in
Turing-subuniversal models of computation. We investigate empirical
distributions of computing models in the Chomsky hierarchy. We introduce
measures of algorithmic probability and algorithmic complexity based upon
resource-bounded computation, in contrast to previously thoroughly investigated
distributions produced from the output distribution of Turing machines. This
approach allows for numerical approximations to algorithmic
(Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a
computational hierarchy. We demonstrate that all these estimations are
correlated in rank and that they converge both in rank and values as a function
of computational power, despite fundamental differences between computational
models. In the context of natural processes that operate below the Turing
universal level because of finite resources and physical degradation, the
investigation of natural biases stemming from algorithmic rules may shed light
on the distribution of outcomes. We show that up to 60\% of the
simplicity/complexity bias in distributions produced even by the weakest of the
computational models can be accounted for by Algorithmic Probability in its
approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity
calculator: http://complexitycalculator.com
P Systems with Minimal Left and Right Insertion and Deletion
Summary. In this article we investigate the operations of insertion and deletion performed at the ends of a string. We show that using these operations in a P systems framework (which corresponds to using specific variants of graph control), computational completeness can even be achieved with the operations of left and right insertion and deletion of only one symbol.
Approximating Language Edit Distance Beyond Fast Matrix Multiplication: Ultralinear Grammars Are Where Parsing Becomes Hard!
In 1975, a breakthrough result of L. Valiant showed that parsing context free grammars can be reduced to Boolean matrix multiplication, resulting in a running time of O(n^omega) for parsing where omega <= 2.373 is the exponent of fast matrix multiplication, and n is the string length. Recently, Abboud, Backurs and V. Williams (FOCS 2015) demonstrated that this is likely optimal; moreover, a combinatorial o(n^3) algorithm is unlikely to exist for the general parsing problem. The language edit distance problem is a significant generalization of the parsing problem, which computes the minimum edit distance of a given string (using insertions, deletions, and substitutions) to any valid string in the language, and has received significant attention both in theory and practice since the seminal work of Aho and Peterson in 1972. Clearly, the lower bound for parsing rules out any algorithm running in o(n^omega) time that can return a nontrivial multiplicative approximation of the language edit distance problem. Furthermore, combinatorial algorithms with cubic running time or algorithms that use fast matrix multiplication are often not desirable in practice.
To break this n^omega hardness barrier, in this paper we study additive approximation algorithms for language edit distance. We provide two explicit combinatorial algorithms to obtain a string with minimum edit distance with performance dependencies on either the number of non-linear productions, k^*, or the number of nested non-linear production, k, used in the optimal derivation. Explicitly, we give an additive O(k^*gamma) approximation in time O(|G|(n^2 + (n/gamma)^3)) and an additive O(k gamma) approximation in time O(|G|(n^2 + (n^3/gamma^2))), where |G| is the grammar size and n is the string length. In particular, we obtain tight approximations for an important subclass of context free grammars known as ultralinear grammars, for which k and k^* are naturally bounded. Interestingly, we show that the same conditional lower bound for parsing context free grammars holds for the class of ultralinear grammars as well, clearly marking the boundary where parsing becomes hard
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
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