Monomial Testing and Applications

Shenshi Chen

Monomial Testing and Applications

Computational Complexity 2013-04-15 v2

Authors: Shenshi Chen

Abstract

In this paper, we devise two algorithms for the problem of testing $q$ -monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$ . One is an $O^*(2^k)$ time randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic algorithm for the same $q$ -monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of $q$ -monomial testing are also given, including a deterministic $O^*(12.8^{mk})$ upper bound for the $m$ -set $k$ -packing problem.

Keywords

computational complexity

Cite

@article{arxiv.1303.0478,
  title  = {Monomial Testing and Applications},
  author = {Shenshi Chen},
  journal= {arXiv preprint arXiv:1303.0478},
  year   = {2013}
}

Comments

17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note: substantial text overlap with arXiv:1302.5898; and text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other authors

Monomial Testing and Applications

Abstract

Keywords

Cite

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