Discrete Mathematics & Theoretical Computer Science
| author: | Karell Bertet and Mirabelle Nebut |
|---|---|
| title: | Efficient Algorithms on the Family Associated to an Implicational System |
| keywords: | lattice, ordered set, Moore family, implicational system, closure operator, algorithm |
| abstract: | An implication system (IS) on a finite set S is a set of rules called Σ-implications of the kind A→ΣB
, with A,B ⊆ S. A subset X ⊆ S
satisfies A →Σ B when ``A ⊆ X implies B
⊆ X'' holds, so ISs can be used to describe constraints
on sets of elements, such as dependency or causality. ISs are
formally closely linked to the well known notions of closure
operators and Moore families. This paper focuses on their
algorithmic aspects. A number of problems issued from an IS
Σ (e.g. is it minimal, is a given implication entailed by the
system) can be reduced to the computation of closures
φΣ(X), where φΣ is the closure
operator associated to Σ. We propose a new approach to compute
such closures, based on the characterization of the direct-optimal
IS Σdo which has the following properties:
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |
| reference: | Karell Bertet and Mirabelle Nebut (2004), Efficient Algorithms on the Family Associated to an Implicational System, Discrete Mathematics and Theoretical Computer Science 6, pp. 315-338 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dm060209.ps.gz (81 K) |
| ps-source: | dm060209.ps (239 K) |
| pdf-source: | dm060209.pdf (220 K) |
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.