Download e-book for kindle: Descriptive Complexity, Canonisation, and Definable Graph by Martin Grohe

By Martin Grohe

Descriptive complexity concept establishes a connection among the computational complexity of algorithmic difficulties (the computational assets required to resolve the issues) and their descriptive complexity (the language assets required to explain the problems). This groundbreaking e-book techniques descriptive complexity from the attitude of contemporary structural graph thought, particularly graph minor conception. It develops a 'definable constitution concept' all in favour of the logical definability of graph theoretic options comparable to tree decompositions and embeddings. the 1st half starts off with an creation to the heritage, from common sense, complexity, and graph concept, and develops the idea as much as first functions in descriptive complexity conception and graph isomorphism trying out. it might function the foundation for a graduate-level direction. the second one half is extra complicated and commonly dedicated to the facts of a unmarried, formerly unpublished theorem: homes of graphs with excluded minors are decidable in polynomial time if, and provided that, they're definable in fixed-point good judgment with counting.

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Descriptive Complexity, Canonisation, and Definable Graph Structure Theory (Lecture Notes in Logic) by Martin Grohe

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