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Monomials, Multilinearity and Identity Testing in Simple ReadRestricted Circuits∗
, 2013
"... We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero. We give a deterministic polynomial time algorithm for this problem when the inputs are readtwice or readthrice formulas. In the process, these algorithms also test if the input circuit is compu ..."
Abstract

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We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero. We give a deterministic polynomial time algorithm for this problem when the inputs are readtwice or readthrice formulas. In the process, these algorithms also test if the input circuit is computing a multilinear polynomial. We further study three related computational problems on arithmetic circuits. Given an arithmetic circuit C, 1) ZMC: test if a given monomial in C has zero coefficient or not, 2) MonCount: compute the number of monomials in C, and 3) MLIN: test if C computes a multilinear polynomial or not. These problems were introduced by Fournier, Malod and Mengel [STACS 2012], and shown to characterize various levels of the counting hierarchy (CH). We address the above problems on readrestricted arithmetic circuits and branching programs. We prove several complexity characterizations for the above problems on these restricted classes of arithmetic circuits.
On enumerating monomials and other combinatorial structures by polynomial interpolation
 THEORY OF COMPUTING SYSTEMS
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