From Holant To #CSP And Back: Dichotomy For Holant$^c$ Problems

We explore the intricate interdependent relationship among counting problems, considered from three frameworks for such problems: Holant Problems, counting CSP and weighted H-colorings. We consider these problems for general complex valued functions that take Boolean inputs. We show that results from one framework can be used to derive results in another, and this happens in both directions. Holographic reductions discover an underlying unity, which is only revealed when these counting problems are investigated in the complex domain C. We prove three complexity dichotomy theorems, leading to a general theorem for Holantc problems. This is the natural class of Holant problems where

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Jin-yi Cai, Sangxia Huang, Pinyan Lu
• Keywords: Complexity Dichotomy Theorems, CORR 2010, Education, Intricate Interdependent Relationship, Problems