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Computing complexity distances between algorithms

Salvador Romaguera, Enrique A. Sánchez-Pérez, Oscar Valero (2003)

Kybernetika

We introduce a new (extended) quasi-metric on the so-called dual p-complexity space, which is suitable to give a quantitative measure of the improvement in complexity obtained when a complexity function is replaced by a more efficient complexity function on all inputs, and show that this distance function has the advantage of possessing rich topological and quasi-metric properties. In particular, its induced topology is Hausdorff and completely regular. Our approach is applied to the measurement...

Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...

Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...

Computing multiple-valued logic programs.

James J. Lu, Jacques Calmet, Joachim Schü (1997)

Mathware and Soft Computing

The logic of signed formula can be used to reason about a wide variety of multiple-valued logics [Häh94b, LMR97]. The formal theoretical foundation of multiple-valued logic programming based on signed formulas is set forth in [Lu96]. The current paper is an investigation into the operational semantics of such signed logic programming. The connection of signed logic programming to constraint logic programming is presented, search space issues are briefly discussed for both general and special cases,...

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