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

By Martin Grohe

ISBN-10: 1107014522

ISBN-13: 9781107014527

Descriptive complexity idea establishes a connection among the computational complexity of algorithmic difficulties (the computational assets required to unravel the issues) and their descriptive complexity (the language assets required to explain the problems). This groundbreaking e-book techniques descriptive complexity from the perspective of contemporary structural graph concept, in particular graph minor idea. It develops a 'definable constitution idea' desirous about the logical definability of graph theoretic options corresponding to tree decompositions and embeddings. the 1st half starts off with an advent to the historical past, from good judgment, complexity, and graph idea, and develops the idea as much as first functions in descriptive complexity concept and graph isomorphism trying out. it may possibly function the foundation for a graduate-level direction. the second one half is extra complex and normally dedicated to the evidence of a unmarried, formerly unpublished theorem: houses of graphs with excluded minors are decidable in polynomial time if, and provided that, they're definable in fixed-point common sense with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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Descriptive Complexity, Canonisation, and Definable Graph Structure Theory (Lecture Notes in Logic) by Martin Grohe

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