Deciding the Vapnik-Červonenkis Dimension is Σp3-complete
نویسنده
چکیده
Linial et al. raised the question of how difficult the computation of the Vapnik-Červonenkis dimension of a concept class over a finite universe is. Papadimitriou and Yannakakis obtained a first answer using matrix representations of concept classes. However, this approach does not capture classes having exponential size, like monomials, which are encountered in learning theory. We choose a more natural representation, which leads us to redefine the vc dimension problem. We establish that vc dimension is Σp3 -complete, thereby giving a rare natural example of a Σ p 3 -complete problem.
منابع مشابه
Deciding the VC Dimension is Σ p 3 - complete , II
The path VC-dimension of a graph G is the size of the largest set U of vertices of G such that each subset of U is the intersection of U with a subpath of G. The VC-dimension for graphs was introduced by Kranakis, et al. [KKR97], building on an idea of Haussler and Welzl [HW87]. We show that computing the path VC-dimension of a graph is Σp3-complete. This adds a rare natural Σ p 3-complete prob...
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