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.

This book constitutes the refereed proceedings of the 4th International Conference on Theory and Applications of Models of Computation, TAMC 2007, held in Shanghai, China in May 2007.

The 67 revised full papers presented together with 2 plenary lectures were carefully reviewed and selected from over 500 submissions. All major areas in computer science, mathematics (especially logic) and the physical sciences particularly with regard to computation and computability theory are addressed. The papers - featuring this crossdisciplinary character - particularly focus on algorithms, complexity and computability theory, giving the conference a special flavor and distinction.

This book constitutes the refereed proceedings of the Third International Conference on Theory and Applications of Models of Computation, TAMC 2006, held in Beijing, China, in May 2006. The 75 revised full papers presented together with 7 plenary talks were carefully reviewed and selected from 319 submissions. All major areas in computer science, mathematics (especially logic) and the physical sciences particularly with regard to computation and computability theory are addressed.

This book constitutes the proceedings of the Second Annual International Conference on Computing and Combinatorics, COCOON '96, held in June 1996 in Hong Kong.
The 44 papers presented in the book in revised version were carefully selected from a total of 82 submissions. They describe state-of-the-art research results from various areas of theoretical computer science, combinatorics related to computing, and experimental analysis of algorithms; computational graph theory, computational geometry, and networking issues are particularly well-presented.