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Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain (Hardcover)
Loot Price: R3,881
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Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain (Hardcover)
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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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