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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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Descriptive Complexity, Canonisation, and Definable Graph Structure Theory (Hardcover)
Loot Price: R4,567
Discovery Miles 45 670
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Descriptive Complexity, Canonisation, and Definable Graph Structure Theory (Hardcover)
Series: Lecture Notes in Logic
Expected to ship within 12 - 17 working days
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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single, previously unpublished theorem: properties of graphs with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.
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