Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain
eBook - PDF

Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain

About this book

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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Table of contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. 1 Counting Problems
  8. 2 Fibonacci Gates and Holant* Problems
  9. 3 Boolean #CSP
  10. 4 Matchgates and Holographic Algorithms
  11. 5 2-Spin Systems on Regular Graphs
  12. 6 Holant Problems and #CSP
  13. 7 Holant Dichotomy for Symmetric Constraints
  14. 8 Planar #CSP for Symmetric Constraints
  15. 9 Planar Holant for Symmetric Constraints
  16. 10 Dichotomies for Asymmetric Constraints
  17. Bibliography
  18. Index

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Yes, you can access Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain by Jin-Yi Cai,Xi Chen in PDF and/or ePUB format, as well as other popular books in Computer Science & Computer Science General. We have over one million books available in our catalogue for you to explore.