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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 ebook methods descriptive complexity from the perspective of contemporary structural graph conception, in particular graph minor thought. It develops a 'definable constitution idea' interested in the logical definability of graph theoretic recommendations equivalent to tree decompositions and embeddings. the 1st half begins with an creation to the history, from common sense, complexity, and graph idea, and develops the idea as much as first purposes in descriptive complexity idea and graph isomorphism trying out. it might probably function the root for a graduate-level direction. the second one half is extra complicated and almost always dedicated to the evidence of a unmarried, formerly unpublished theorem: homes of graphs with excluded minors are decidable in polynomial time if, and provided that, they're definable in fixed-point common sense with counting.

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