Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain

Nonfiction, Science & Nature, Mathematics, Number Theory, Computers, General Computing
Cover of the book Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain by Jin-Yi Cai, Xi Chen, Cambridge University Press
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Author: Jin-Yi Cai, Xi Chen ISBN: 9781108505840
Publisher: Cambridge University Press Publication: November 16, 2017
Imprint: Cambridge University Press Language: English
Author: Jin-Yi Cai, Xi Chen
ISBN: 9781108505840
Publisher: Cambridge University Press
Publication: November 16, 2017
Imprint: Cambridge University Press
Language: English

Complexity theory aims to understand and classify computational problems, especially decision problems, according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems. The authors present dichotomy classifications for broad classes of counting problems in the realm of P and NP. Classifications are proved for partition functions of spin systems, graph homomorphisms, constraint satisfaction problems, and Holant problems. The book assumes minimal prior knowledge of computational complexity theory, developing proof techniques as needed and gradually increasing the generality and abstraction of the theory. This volume presents the theory on the Boolean domain, and includes a thorough presentation of holographic algorithms, culminating in classifications of computational problems studied in exactly solvable models from statistical mechanics.

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Complexity theory aims to understand and classify computational problems, especially decision problems, according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems. The authors present dichotomy classifications for broad classes of counting problems in the realm of P and NP. Classifications are proved for partition functions of spin systems, graph homomorphisms, constraint satisfaction problems, and Holant problems. The book assumes minimal prior knowledge of computational complexity theory, developing proof techniques as needed and gradually increasing the generality and abstraction of the theory. This volume presents the theory on the Boolean domain, and includes a thorough presentation of holographic algorithms, culminating in classifications of computational problems studied in exactly solvable models from statistical mechanics.

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