Abstract
Given a monomial ideal \(I=\langle{m_1,m_2,\cdots,m_k}\rangle\), where m i are monomials, and a polynomial f as an arithmetic circuit the monomial Ideal Membership Problem is to test if f ∈ I. We show that the problem has a randomized polynomial time algorithm for constant k. Furthermore, if k is constant and f is computed by a ΣΠ Σ circuit with output gate of bounded fanin then we can test whether f ∈ I in deterministic polynomial time.
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Arvind, V., Mukhopadhyay, P. (2007). The Monomial Ideal Membership Problem and Polynomial Identity Testing. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_69
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DOI: https://doi.org/10.1007/978-3-540-77120-3_69
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77118-0
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