Classification of a Class of Counting Problems Using Holographic Reductions

Authors:
Michael Kowalczyk
Affiliations:
Department of Mathematics and Computer Science, Northern Michigan University, Marquette 49855
Venue:
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Year:
2009

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Abstract

The purpose of this work is to prove a generalization of the dichotomy theorem from [6], extending that result to a larger class of counting problems. This is achieved through the use of interpolation and holographic reductions. We also use holographic reductions to establish a close connection between a class of problems which are solvable using Fibonacci gates and the class of problems which can be solved by applying a particular kind of counting argument.