12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

Rational Cubic Ball Interpolants For Shape Preserving Curves And Surfaces

Interpolan pengekalan bentuk adalah satu teknik rekabentuk lengkung/ permukaan yang sangat penting dalam CAD/-CAM dan rekabentuk geometric Shape preserving interpolation is an essential curve/surface design technique in CAD/CAM and geometric desig

Piecewise polynomial monotonic interpolation of 2D gridded data

International audienceA method for interpolating monotone increasing 2D scalar data with a monotone piecewise cubic C$^1$-continuous surface is presented. Monotonicity is a sufficient condition for a function to be free of critical points inside its domain. The standard axial monotonicity for tensor-product surfaces is however too restrictive. We therefore introduce a more relaxed monotonicity constraint. We derive sufficient conditions on the partial derivatives of the interpolating function to ensure its monotonicity. We then develop two algorithms to effectively construct a monotone C$^1$ surface composed of cubic triangular Bézier surfaces interpolating a monotone gridded data set. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain. Numerical examples are given to illustrate the performance of the algorithm

Where Fail-Safe Default Logics Fail

Reiter's original definition of default logic allows for the application of a default that contradicts a previously applied one. We call failure this condition. The possibility of generating failures has been in the past considered as a semantical problem, and variants have been proposed to solve it. We show that it is instead a computational feature that is needed to encode some domains into default logic

Positivity preservation of implicit discretizations of the advection equation

We analyze, from the viewpoint of positivity preservation, certain discretizations of a fundamental partial differential equation, the one-dimensional advection equation with periodic boundary condition. The full discretization is obtained by coupling a finite difference spatial semidiscretization (the second- and some higher-order centered difference schemes, or the Fourier spectral collocation method) with an arbitrary _x0012_θ-method in time (including the forward and backward Euler methods, and a second-order method by choosing _x0012_ θ ∈ [0, 1] suitably). The full discretization generates a two-parameter family of circulant matrices M ∈ ℝ m_x0002_xm , where each matrix entry is a rational function in θ and _x0017_ν . Here, _x0017_ν denotes the CFL number, being proportional to the ratio between the temporal and spatial discretization step sizes. The entrywise non-negativity of the matrix M---which is equivalent to the positivity preservation of the fully discrete scheme---is investigated via discrete Fourier analysis and also by solving some low-order parametric linear recursions. We find that positivity preservation of the fully discrete system is impossible if the number of spatial grid points m is even. However, it turns out that positivity preservation of the fully discrete system is recovered for odd values of m provided that θ ≥ 1/2 and ν are chosen suitably. These results are interesting since the systems of ordinary differential equations obtained via the spatial semi-discretizations studied are not positivity preserving

Tractable Optimization Problems through Hypergraph-Based Structural Restrictions

Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal solution is an NP-hard problem in general; yet, when restricted over classes of instances whose constraint interactions can be modelled via (nearly-)acyclic graphs, this problem is known to be solvable in polynomial time. In this paper, larger classes of tractable instances are singled out, by discussing solution approaches based on exploiting hypergraph acyclicity and, more generally, structural decomposition methods, such as (hyper)tree decompositions