Algorithmic Combinatorics on Partial Words

Francine Blanchet-Sadri

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November 19, 2007 by Chapman and Hall/CRC
Reference - 392 Pages - 69 B/W Illustrations
ISBN 9781420060928 - CAT# C6092
Series: Discrete Mathematics and Its Applications

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Features

  • Presents algorithms in English followed by pseudo code to facilitate implementation of the algorithms
  • Provides abundant worked examples and diagrams to illustrate concepts
  • Offers links to many web interfaces that have been established for automated use of the programs related to the book
  • Contains numerous exercises, including programming exercises, at the end of each chapter as well as selected solutions at the back of the book
  • Summary

    The discrete mathematics and theoretical computer science communities have recently witnessed explosive growth in the area of algorithmic combinatorics on words. The next generation of research on combinatorics of partial words promises to have a substantial impact on molecular biology, nanotechnology, data communication, and DNA computing. Delving into this emerging research area, Algorithmic Combinatorics on Partial Words presents a mathematical treatment of combinatorics on partial words designed around algorithms and explores up-and-coming techniques for solving partial word problems as well as the future direction of research.

    This five-part book begins with a section on basics that covers terminology, the compatibility of partial words, and combinatorial properties of words. The book then focuses on three important concepts of periodicity on partial words: period, weak period, and local period. The next part describes a linear time algorithm to test primitivity on partial words and extends the results on unbordered words to unbordered partial words while the following section introduces some important properties of pcodes, details a variety of ways of defining and analyzing pcodes, and shows that the pcode property is decidable using two different techniques. In the final part, the author solves various equations on partial words, presents binary and ternary correlations, and covers unavoidable sets of partial words.

    Setting the tone for future research in this field, this book lucidly develops the central ideas and results of combinatorics on partial words.