Resolution lower bounds for perfect matching principles
نویسندگان
چکیده
منابع مشابه
Resolution Lower Bounds for Perfect Matching Principles
For an arbitrary hypergraph H, let PM(H) be the propositional formula asserting that H contains a perfect matching. We show that every resolution refutation of PM(H) must have size exp ( Ω ( δ(H) λ(H)r(H)(log n(H))(r(H) + log n(H)) )) , where n(H) is the number of vertices, δ(H) is the minimal degree of a vertex, r(H) is the maximal size of an edge, and λ(H) is the maximal number of edges incid...
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The resolution complexity of the perfect matching principle was studied by Razborov [14], who developed a technique for proving its lower bounds for dense graphs. We construct a constant degree bipartite graph Gn such that the resolution complexity of the perfect matching principle for Gn is 2 where n is the number of vertices in Gn. This lower bound is tight up to some polynomial. Our result i...
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We consider three restrictions on Boolean circuits: bijectivity, consistency and mul-tilinearity. Our main result is that Boolean circuits require exponential size to compute the bipartite perfect matching function when restricted to be (i) bijective or (ii) consistent and multilinear. As a consequence of the lower bound on bijec-tive circuits, we prove an exponential size lower bound for monot...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2004
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2004.01.004