The Incremental Satisfiability Problem for a Two Conjunctive Normal Form

We propose a novel method to review K ⊢ φ when K and φ are both in Conjunctive Normal Forms (CF). We extend our method to solve the incremental satisfiablity problem (ISAT), and we present different cases where ISAT can be solved in polynomial time. Especially, we present an algorithm for 2-ISAT. Our last algorithm allow us to establish an upper bound for the time-complexity of 2-ISAT, as well as to establish some tractable cases for the 2-ISAT problem

Low-Exponential Algorithm for Counting the Number of Edge Cover on Simple Graphs

A procedure for counting edge covers of simple graphs is presented. The procedure splits simple graphs into non-intersecting cycle graphs. This is a “low exponential” exact algorithm to count edge covers for simple graphs whose upper bound in the worst case is O(1.465575(m−n) × (m + n)), where m and n are the number of edges and nodes of the input graph, respectively

Caracterización de complejidad semántica en pasajes tipo TOEFL

Reading comprehension is a process that involves the realization of mental models, as well as the storage of memories in long-term memory; if we add to this that many students need to accredit other languages, it involves performing more cognitive processes. With mental models, it is possible to analyze the internal structures present, for example, in the reading comprehension section of the TOEFL test where three types of texts are involved: narrative, expository and argumentative. In this work, the three types of texts are semantically modeled as structures, where semantic relations are the input for their construction, and the semantic complexity depending on text type to be reviewed. By having these structures, students can graphically locate the elements that characterize each type of text, and an orientation is given to generate expert systems for the training of the activities to be developed.La comprensión lectora es un proceso que implica la realización de modelos mentales, así como el almacenamiento de recuerdos en la memoria a largo plazo, sí a esto le agregamos que muchos estudiantes requieren acreditar otros idiomas, implica realizar más procesos cognitivos. Con los modelos mentales se pueden analizar las estructuras internas presentes, por ejemplo, en la sección de comprensión lectora del examen TOEFL donde se involucran tres tipos de textos: narrativos, expositivos, y argumentativos. En este trabajo se modelan semánticamente los tres tipos de textos como estructuras, donde las relaciones semánticas son el insumo para la construcción de estas, así como la complejidad semántica dependiendo del tipo de texto a revisar. Al contar con dichas estructuras los estudiantes pueden ubicar gráficamente los elementos que caracterizan a cada tipo de texto, así como se da una orientación para generar sistemas expertos para el entrenamiento de las actividades a desarrollar

A New Optimization Strategy for Solving the Fall-Off Boundary Value Problem in Pixel-Value Di®erencing Steganography

In Digital Image Steganography, Pixel-Value Di®erencing (PVD) methods use the di®erence between neighboring pixel values to determine the amount of data bits to be inserted. The main advantage of these methods is the size of input data that an image can hold. However, the fall- o® boundary problem and the fall in error problem are persistent in many PVD steganographic methods. This results in an incorrect output image. To ¯x these issues, usually the pixel values are either somehow adjusted or simply not considered to carry part of the input data. In this paper, we enhance the Tri-way Pixel-Value Di®erencing method by ¯nding an optimal pixel value for each pixel pair such that it carries the maximum input data possible without ignoring any pair and without yielding incorrect pixel values

Propuestas Algorítmicas para la Resolución de los Problemas de Satisfactibilidad

Abstract. En esta investigación doctoral se analizaron los problemas de satisfactibilidad en el cálculo proposicional. Como resultado del análisis se diseñaron y construyeron diversas propuestas algorítmicas para la resolución de tales problemas. Enfasis especial se puso en la determinación de la complejidad en tiempo de los peores casos que aparecen al trabajar con las propuestas algorítmicas

Approximation Algorithms for MaxSAT

The main aim of NP-completeness theory is the analysis of intractability

Approximation algorithms for MaxSAT

The main aim of NP-completeness theory is the analysis of intractability. Many optimization problems were first proved to be NP-hard. Since the complete solution of these problems requires exponential time, polynomial time algorithms to find "near-optimal" solutions, i.e., approximation algorithms, appear to be viable. In this paper we show the basic principles of Approximation Theory for NP-completeness and sketch a collection of algorithms

A Polynomial Graphical Reduction to Speed Up the Counting of Models for Boolean Formulas

Abstract. In this paper, we focus on exact, deterministic algorithms for computing the number of models in Boolean formulas in Two Conjuntive Form (2-CF), denoted as #2-SAT problem. We present a series of linear procedures which when they are integrated into a main program, allow us to compute in polynomial time the number of models of a formula F in 2-CF when the constraint graph GF holds the following condition: GF canbereducedtoonefreetreejoinedwitha set of fundamental cycles, and such that those cyles are non-intersected (any pair of cycles do not share edges) or, they are intersected in just one edge. The resulting method for counting models in a 2-CF could be used to impact directly in the reduction of the complexity time of the algorithms for other counting problems

Polynomial Strategies for the 3-Coloring of a Graph

El coloreo de un grafo es un problema de interés en el área de las ciencias de la computación debido a las muchas aplicaciones que este ofrece. El problema de coloreo de un grafo tiene varias aplicaciones en áreas como en el problema de asignación de tareas, asignación de frecuencias, planeación, etc. En el coloreo de un grafo, se asigna un color apropiado a los nodos (de forma que dos nodos adyacentes no tengan igual color), usando el menor numero posible de colores. Se presentan algunas condiciones necesarias para el 3-coloreo de un grafo de entrada, todas esas condiciones se pueden comprobar en tiempo polinomial.También se propone un patrón combinatorio apropiado para la representación del 3-coloreo de un grafo basado en sus ciclos básicos, y donde dicho patrón es codificado a través de la satisfactibilidad de una formula booleana en dos forma conjuntiva. La formula booleana es formada de acuerdo a los ciclos básicos presentes en el grafo. En este artículo se presenta una metodología para el 3-coloreo de un grafo utilizando 2-CF (dos forma conjuntiva), así como su cálculo por medio de ejemplos.The coloring of a graph is a problem of interest in the area of computer science due to the many applications it offers. The graph coloring problem has many utilities in areas like scheduling problems, frequency allocation, planning, etc. In the coloring of a graph, we want to color the nodes properly with the smallest possible number of colors. We present some necessary conditions for the 3-coloring of an input graph. All of those conditions can be checked in polynomial time. We also propose an appropriate combinatorial pattern representing proper 3-coloring of a graph based in its basic cycles, and where such pattern is codified via satisfy assignments of a two conjunctive Boolean formula. The Boolean formula is formed according to the basic cycles appearing in the graph. This paper shows the methodology for 3-coloring of a graph using 2-CF (Conjunctive form), as well as by several examples illustrate the calculation of it

Algorithm to Count the Number of Signed Paths in an Electrical Network via Boolean Formulas

Este artículo presenta un método práctico para contar los diferentes caminos signados los cuales mantienen una carga eléctrica sobre cada una de las líneas de una red eléctrica. Consideramos que hay sólo una carga (positiva o negativa) en cada nodo de la red. Nosotros modelamos el problema de contar los caminos signados vía el problema #2SAT. El problema #2SAT consiste en contar modelos de fórmulas booleanas en dos forma conjuntiva. Nuestro método esta basado en la topología del grafo que representa la red eléctrica y de la cual se obtiene su fórmula booleana en dos forma conjuntiva. Un conjunto de ecuaciones de recurrencia son aplicadas, partiendo de los nodos terminales hacia el nodo raíz de la red. Tales ecuaciones de recurrencianos permiten calcular el valor #2SAT para la fórmula asociada a la red eléctrica. El valor calculado (#2SAT) representa las diferentes formas de mantener carga sobre todas las líneas dela red eléctrica.This article presents a practical method to count the different signed paths which maintain an electric charge on each one of the lines of an electrical network. We assume that there is just one charge (positive or negative) on each network node. We model the problem of counting the signed paths via the #2SAT problem. The #2SAT problem consists on counting models of Boolean formulas in two conjunctive forms. Our method is based on the topology of the graph representing the electrical network and from which we get its Boolean formula in two conjunctive form. A set of recurrence equations are applied, starting from the terminal nodes up to the root node of the network. Such recurrence equations allow us to compute #2SAT for the formula associated to the electrical network. The computed value (#2SAT) represents the different ways to keep charge on all line of the electrical network