ENGLISH

Descriptive Complexity, Canonisation, and Definable Graph Structure Theory

By Martin Grohe

Book information

Publisher
Cambridge University Press
Year
2017
ISBN
1107014522, 9781107014527
Language
english
Format
PDF
Filesize
5 MB (5322212 bytes)
Series
Lecture Notes in Logic
Pages
554\551
Topic
Mathematics Logic
Time added
2017-09-22 08:28:56
Logic;Pure Mathematics;Mathematics;Science & Math;Used & Rental Textbooks;Specialty Boutique

Description

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 The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.

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