33 research outputs found
PURL: A new polynomial-time solvable class of satisfiability
In this work a new polynomial-time solvable class of satisfiability PURL
( PropUnit RemoveLiterals) is presented, based on natural extensions of the known con cepts of the l-neighbourhood of a clause and removable literal. The algorithm Remove Literals is also shown which determines if a formula in PURL is satisfiable. The PURL
class is a proper superset of all previously known polynomial-time solvable classes. The
study of this class is motivated by the resolution of geometric problems.Junta de AndalucÃa PAI-FQM-016
Fuzzy logic programs as hypergraphs. Termination results
Graph theory has been a useful tool for logic programming in many aspects. In this paper, we propose an equivalent representation of multi-adjoint logic programs using hypergraphs, which are a generalization of classical graphs that allows the use of hypergraph theory in logic programming. Specifically, this representation has been considered in this paper to increase the level and flexibility of different termination results of the computation of the least model of fuzzy logic programs via the immediate consequence operator. Consequently, the least model of more general and versatile fuzzy logic programs can be obtained after finitely many iterations, although infinite programs or programs with loops and general aggregators will be consideredAgencia Estatal de Investigación PID2019-108991GB-I00Junta de AndalucÃa FEDER-UCA18-108612European Union COST Action CA1712
Entanglement in eight-qubit graph states
Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we
obtain a representative which requires the minimum number of controlled-Z gates for its preparation, and calculate the Schmidt measure for the 8-partite split,
and the Schmidt ranks for all bipartite splits. This results into an extension to 8 qubits of the classification of graph states proposed by Hein, Eisert, and Briegel
[M. Hein, J. Eisert, H.J. Briegel, Phys. Rev. A 69 (2004) 062311].Junta de AndalucÃa P06-FQM-02243Ministerio de Ciencia e Innovación FIS2008-05596Junta de AndalucÃa PAI-FQM-0239Junta de AndalucÃa P06-FQM-01649Ministerio de Educación y Ciencia MTM2008-05866-C03-01Junta de AndalucÃa PAI-FQM-016
Informational structures: A dynamical system approach for integrated information
Integrated Information Theory (IIT) has become nowadays the most sensible general theory of consciousness. In addition to very important statements, it opens the door for an abstract (mathematical) formulation of the theory. Given a mechanism in a particular state, IIT identifies a conscious experience with a conceptual structure, an informational object which exists, is composed of identified parts, is informative, integrated and maximally irreducible. This paper introduces a space-time continuous version of the concept of integrated information. To this aim, a graph and a dynamical systems treatment is used to define, for a given mechanism in a state for which a dynamics is settled, an Informational Structure, which is associated to the global attractor at each time of the system. By definition, the informational structure determines all the past and future behavior of the system, possesses an informational nature and, moreover, enriches all the points of the phase space with cause-effect
power by means of its associated Informational Field. A detailed description of its inner structure by invariants and connections between them allows to associate a transition probability matrix to each informational structure and to develop a measure for the level of integrated information of the system.Ministerio de EconomÃa, Industria y CompetitividadJunta de AndalucÃaFondo Europeo de Desarrollo Regiona
Single bend wiring on surfaces
The following problem of rectilinear routing is studied: given pairs of points on a surface and a set of permissible orthogonal paths joining them, whether is it possible to choose a path for each pair avoiding all intersections. We prove that if each pair has one or two possible paths to join it, then the problem is solvable in quadratic time, and otherwise it is NP-complete. From that result, we will obtain that the problem of finding a surface of minimum genus on which the wires can be laid out with only one bend is NP-hard
Labeling Subway Lines
Graphical features on map, charts, diagrams and graph drawings usually must be annotated with text labels in order to convey their meaning. In this paper we focus on a problem that arises when labeling schematized maps, e.g. for subway networks. We present algorithms for labeling points on a line with axis-parallel rectangular labels of equal height. Our aim is to maximize label size under the constraint that all points must be labeled.
Even a seemingly strong simplification of the general point-labeling problem, namely to decide whether a set of points on a horizontal line can be labeled with sliding rectangular labels, turns out to be weakly NPcomplete. This is the first labeling problem that is known to belong to this class. We give a pseudo-polynomial time algorithm for it.
In case of a sloping line points can be labeled with maximum-size square labels in O(n log n) time if four label positions per point are allowed and in O(n 3 log n) time if labels can slide. We also investigate rectangular labels
An algorithm that constructs irreducible triangulations of once-punctured surfaces
A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with precisely one boundary component.Plan Andaluz de Investigación (Junta de AndalucÃa
Towards the Use of Hypergraphs in Multi-adjoint Logic Programming
The representation of a logic program by a graph is a useful procedure in
order to obtain interesting properties of the program and in the computation of the
least model, when it exists. In this paper, we consider hypergraphs for representing
multi-adjoint logic programs and, based on this representation, the hypotheses of an
interesting termination result have been weakened
Monochromatic geometric k-factors for bicolored point sets with auxiliary points
Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms for constructing those k-factors, and gives bounds on the number of auxiliary points needed to draw a monochromatic geometric planar k-factor of S
Monochromatic geometric k-factors in red-blue sets with white and Steiner points
We study the existence of monochromatic planar geometric k-factors on sets of red and blue points. When it is not possible to find a k-factor we make use of auxiliary points: white points, whose position is given as a datum and which color is free; and Steiner points whose position and color is free. We present bounds on the number of white and/or Steiner points necessary and/or sufficient to draw a monochromatic planar geometric k-factor