Results

**1 - 3**of**3**### Incompleteness, Complexity, Randomness and Beyond

, 2001

"... The Library is composed of an... infinite number of hexagonal galleries... [it] includes all verbal structures, all variations permitted by the twenty-five orthographical symbols, but not a single example of absolute nonsense.... These phrases, at first glance incoherent, can no doubt be justified i ..."

Abstract
- Add to MetaCart

(Show Context)
The Library is composed of an... infinite number of hexagonal galleries... [it] includes all verbal structures, all variations permitted by the twenty-five orthographical symbols, but not a single example of absolute nonsense.... These phrases, at first glance incoherent, can no doubt be justified in a cryptographical or allegorical manner; such a justification is verbal and, ex hypothesi, already figures in the Library.... The certitude that some shelf in some hexagon held precious books and that these precious books were inaccessible seemed almost intolerable. A blasphemous sect suggested that... all men should juggle letters and symbols until they constructed, by an improbable gift of chance, these canonical books... but the Library is... useless, incorruptible, secret. Jorge Luis Borges, “The Library of Babel” Gödel’s Incompleteness Theorems have the same scientific status as Einstein’s principle of relativity, Heisenberg’s uncertainty principle, and Watson and Crick’s double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.

### Centre for Discrete Mathematics and Theoretical Computer ScienceSearching for Spanning k-Caterpillars and k-Trees

, 2008

"... We consider the problems of finding spanning k-caterpillars and k-trees in graphs. We first show that the problem of whether a graph has a spanning k-caterpillar is NP-complete, for all k ≥ 1. Then we give a linear time algorithm for finding a spanning 1-caterpillar in a graph with treewidth k. Also ..."

Abstract
- Add to MetaCart

(Show Context)
We consider the problems of finding spanning k-caterpillars and k-trees in graphs. We first show that the problem of whether a graph has a spanning k-caterpillar is NP-complete, for all k ≥ 1. Then we give a linear time algorithm for finding a spanning 1-caterpillar in a graph with treewidth k. Also, as a generalized versions of the depth-first search and the breadth-first search algorithms, we introduce the k-tree search (KTS) algorithm and we use it in a heuristic algorithm for finding a large k-caterpillar in a graph. 1