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Other titles in the Discrete Mathematics and Its Applications series:
Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)by Francine Blanchet-sadri
Synopses & Reviews
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.
The study of combinatorics on words is a relatively new research area in the fields of discrete and algorithmic mathematics. Featuring a simple, accessible style, Algorithmic Combinatorics on Partial Words presents combinatorial and algorithmic concepts in the emerging field of words and partial words. This book contains a wealth of exercises and problems that assists with a variety of algorithm tracing, algorithm design, mathematical proofs, and program implementation. It also includes numerous worked example and diagrams, making this a valuable text for students, researchers, and practitioners seeking to understand this complex subject where many problems remain unexplored.
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