Emergent Mind
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 $O*(2k)$ time randomized algorithm. The other is an $O*(12.8k)$ 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.
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