Identity Testing, Multilinearity Testing, and Monomials in Read-Once/Twice Formulas and Branching Programs

  • Meena Mahajan
  • B. V. Raghavendra Rao
  • Karteek Sreenivasaiah
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero (ACIT). We give a deterministic polynomial time algorithm for this problem when the inputs are read-twice formulas. This algorithm also computes the MLIN predicate, testing if the input circuit computes a multilinear polynomial.

We further study two 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, and 2) MonCount: compute the number of monomials in C. 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 read-restricted arithmetic circuits and branching programs. We prove several complexity characterizations for the above problems on these restricted classes of arithmetic circuits.


Arithmetic Circuit Lower Common Ancestor Lower Common Ancestor Multilinear Polynomial Arithmetic Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Meena Mahajan
    • 1
  • B. V. Raghavendra Rao
    • 2
  • Karteek Sreenivasaiah
    • 1
  1. 1.Institute of Mathematical SciencesChennaiIndia
  2. 2.Saarland UniversitySaarbrückenGermany

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