Lecture 16 : CS 880 : Complexity of Counting Problems
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چکیده
03/15/2012 Lecture 16: CS 880: Complexity of Counting Problems Instructor: Jin-Yi Cai Scribe: Chen Zeng For a symmetric, bipartite matrix A ∈ C, we want to prove the following theorem: Theorem 1. If EVAL(A) is not #P-hard, then there exists an m × m purified bipartite matrix A such that EVAL(A) ≡ EVAL(A). Recall the definition of the purified bipartite matrix : Definition 1. Let A ∈ C be a symmetric, connected and bipartite matrix. A is called a purified bipartite matrix if there exists positive rational numbers μ1, . . . , μm, and an integer 1 ≤ k < m such that A = (
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