Descriptive Complexity, Canonisation, and Definable Graph Structure Theory
By:Martin Grohe
Published on 2017-07-31 by Cambridge University Press
Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.
This Book was ranked at 28 by Google Books for keyword Math book.
Book ID of Descriptive Complexity, Canonisation, and Definable Graph Structure Theory's Books is RLYrDwAAQBAJ, Book which was written byMartin Grohehave ETAG "B0Ag0Hmkz68"
Book which was published by Cambridge University Press since 2017-07-31 have ISBNs, ISBN 13 Code is 9781107014527 and ISBN 10 Code is 1107014522
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