COMPLEXITY OF COUNTING

Date
2013
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Haverford College. Department of Computer Science
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Thesis
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Award
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eng
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Open Access
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Abstract
In this paper, we consider two problems related to counting problems in complexity theory. First, we use the reachability method to prove that nondeterministic logarithm space is closed under complement. Then, we consider the graph matching problem and explain the FKT algorithm which counts the number of the perfect matchings in a planar graph in polynomial time. The general result of counting perfect matchings is known as the PERMANENT problem, which Valiant proved to be #P-complete.
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