Functional first order definability of LRTp

The language LRTp is a non-deterministic language for exact real number computation. It has been shown that all computable rst order relations in the sense of Brattka are denable in the language. If we restrict the language to single-valued total relations (e.g. functions), all polynomials are denable in the language. This paper is an expanded version of [12] in which we show that the non-deterministic version of the limit operator, which allows to dene all computable rst order relations, when restricted to single-valued total inputs, produces single-valued total outputs. This implies that not only the polynomials are denable in the language but also allcomputable rst order functions

Computing the Clique-width of Cactus Graphs

Similar to the tree-width (twd), the clique-width (cwd) is an invariant of graphs. A well known relationship between tree-width and clique-width is that cwd(G) ≤ 3 · 2twd(G)−1. It is also known that tree-width of Cactus graphs is 2, therefore the clique-width for those graphs is smaller or equal than 6. In this paper, it is shown that the clique-width of Cactus graphs is smaller or equal to 4 and we present a polynomial time algorithm which computes exactly a 4-expression

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

Reversibility for Quantum Programming Language QML

We present an extension of the denotational semantic model of the quantum programming language QML, to which computational reversibility is incorporated. The semantics of QML is defined in a functional setting which consider classical and quantum data, to which we add inverse functions. Additionally we incorporate into the semantics a history track which allows reversibility in QML. From the generation and processing of the history track and the final result of a program, the rules for executing reversibility allow to compute the original input data. This work contributes to the study of reversibility in quantum programming languages and considering that there is not yet a quantum computer in which the language can be implemented, this history and the proposed inverse functions are not trivial and allows us to determine that this language is reversible

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

Extremsl Polygonal Arrays for the Merrifield-Simmons Index

For any polygonal array, independently of the number of sides on each polygon the zig-zag polygonal array has the extremal minimum value for the Merrifield-Simmons index. This result generalises a well known fact obtained for hexagonal chains

Extremsl Polygonal Arrays for the Merrifield-Simmons Index

For any polygonal array, independently of the number of sides on each polygon the zig-zag polygonal array has the extremal minimum value for the Merrifield-Simmons index. This result generalises a well known fact obtained for hexagonal chains

Extremsl Polygonal Arrays for the Merrifield-Simmons Index

For any polygonal array, independently of the number of sides on each polygon the zig-zag polygonal array has the extremal minimum value for the Merrifield-Simmons index. This result generalises a well known fact obtained for hexagonal chains

Exteding Extremal Polygonal Arrays for the Meriifield-Simmons Index

Polygonal array graphs have been widely investigated, and they represent a relevant area of interest in mathematical chemistry because they have been used to study intrinsic properties of molecular graphs. For example, to determine the Merrifield-Simmons index of a polygonal array An that is the number of independent sets of that graph, denoted as i(An)