A Boolean Chitrakavya

Abstract— The research work presents the transformation of an integer represented in the binary field of ones and zeros to an other integer by arranging the bits of the number on a m x n matrix and performing a knight’s tour on it and finding the numbers which when transformed produce the same number, i.e., itself. The scheme has been generalized for an integer of m x n bits arranged on a m x n matrix and performing all the possible solution for knight’s tour for a m x n matrix.

Finding Knight’s Tours on an M x N Chessboard With  0 (MN) Hysteresis

Abstract- How can a knight he moved on a chessboard so that the
Knight visits each square once and only once and goes hack to the starting square? The earliest serious attempt to find a knight’s tour on the chessboard was made by L. Euler in 1759. In this correspondence, a parallel algorithm based on the hysteresis McCulloch-Pith neurons is proposed to solve the knight’s tour problem. The relation between the travelling salesman problem and the knight’s tour problem is also discussed. A large number of simulation runs were performed to investigate the behaviour of the hysteresis McCulloch-Pitts neural model. The purpose of this correspondence is to present a case study-how to successfully represent the combinatorial optimization problems by means of neural network.

The Knight's Tour -Evolutionary vs. Depth-First Search

Abstract-A genetic algorithm is used lo find solutions b the standard 8x8 knight's tour problem, and its performance is compared against standard depth-first search with backtracking. The binary encoding is described, along with a simple repair technique which can be used to extend burs that have reached impasse. The repair method is powerful enough on its own to find complete tours, given randomly generated bit strings. But when used in conjunction with a genetic algorithm , considerably more solutions are found. Depth-first search is shown to find more solutions under certain  conditions , but the genetic algorithm finds solutions more consistently for arbitrary initial conditions.

Context-Free Representational Under specification For NLG

The purpose of the COGENT Project1 is to look at issues in generic (wide-coverage and reusable) surface generation. Central to generic generation is the issue of nondeterminism, i.e. multiple outputs for the same input, and how to control it. Nondeterminism arises from three main sources in natural language generation2:

(i) wide syntactic and lexical coverage: the wider the coverage of grammar and lexicon, the more word strings can be generated from the same semantic representation;

(ii) underdetermined inputs: the less specific the semantic or conceptual representation, the
more word strings correspond to it; and

(iii) unconstrained mapping from inputs to realisations: the fewer constraints
(e.g. rule application conditions, intermediate selection processes, probabilities) there are, the more realisations can be generated from an input. Wide coverage and (even extensively) underdetermined semantics can both make an NLG system more generic, because they help make a system more portable and reusable. However, at present no comprehensive methodology for controlling the nondeterminism, for deciding between alternatives, exists. It is one of the core aims of COGENT to develop such a methodology.

Heurististics as an Aid To Back Tracking, a Classroom Project

Abstract- The knight's tour problem is discussed as a classroom example of a backtracking problem which requires heuristics to be effective.

Boosting Combinatorial Search Through Randomization (gomes)

Abstract :Unpredictability in the running time of complete search procedures can often be explained by the phenomenon of “heavy-tailed cost distributions”, meaning that at any time
during the experiment there is a non-negligible probability of hitting a problem that requires exponentially more time to solve than any that has been encountered before (Gomes et
al. 1998a). We present a general method for introducing controlled randomization into complete search algorithms. The “boosted” search methods provably eliminate heavy-tails to
the right of the median. Furthermore, they can take advantage of heavy-tails to the left of the median (that is, a nonnegligible chance of very short runs) to dramatically shorten the solution time. We demonstrate speedups of several orders of magnitude for state-of-the-art complete search procedures running on hard, real-world problems.