English

Expressing Linear Orders Requires Exponential-Size DNNFs

Computational Complexity 2019-05-31 v3 Artificial Intelligence Logic in Computer Science

Abstract

We show that any DNNF circuit that expresses the set of linear orders over a set of nn candidates must be of size 2Ω(n)2^{\Omega(n)}. Moreover, we show that there exist DNNF circuits of size 2O(n)2^{O(n)} expressing linear orders over nn candidates.

Cite

@article{arxiv.1807.06397,
  title  = {Expressing Linear Orders Requires Exponential-Size DNNFs},
  author = {Ronald de Haan},
  journal= {arXiv preprint arXiv:1807.06397},
  year   = {2019}
}
R2 v1 2026-06-23T03:04:13.797Z