computational complexity

, Volume 24, Issue 1, pp 1–30 | Cite as

Monomials in Arithmetic Circuits: Complete Problems in the Counting Hierarchy

  • Hervé Fournier
  • Guillaume MalodEmail author
  • Stefan Mengel


We consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems are complete for subclasses of the counting hierarchy which had few or no known natural complete problems before. We also study these questions for circuits computing multilinear polynomials and for univariate multiplicatively disjoint circuits.


Arithmetic circuits counting problems polynomials 

Subject classification

68Q15 68Q17 03D15 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Hervé Fournier
    • 1
  • Guillaume Malod
    • 2
    Email author
  • Stefan Mengel
    • 3
  1. 1.Institut de Mathématiques de Jussieu, UMR 7586 CNRSUniv Paris Diderot, Sorbonne Paris CitéParisFrance
  2. 2.Institut de Mathématiques de Jussieu, UMR 7586 CNRSUniversity Paris Diderot, Sorbonne Paris CitéParisFrance
  3. 3.LIX, École PolytechniquePalaiseauFrance

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