Expressing Linear Orders Requires Exponential-Size DNNFs

July 17, 2018 ยท The Ethereal ยท ๐Ÿ› arXiv.org

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Authors Ronald de Haan arXiv ID 1807.06397 Category cs.CC: Computational Complexity Cross-listed cs.AI, cs.LO Citations 0 Venue arXiv.org Last Checked 3 months ago
Abstract
We show that any DNNF circuit that expresses the set of linear orders over a set of $n$ candidates must be of size $2^{ฮฉ(n)}$. Moreover, we show that there exist DNNF circuits of size $2^{O(n)}$ expressing linear orders over $n$ candidates.
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