Monomials in arithmetic circuits: Complete problems in the counting hierarchy

Hervé Fournier (1) , Guillaume Malod , Stefan Mengel

1 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation

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.

Mots clés: arithmetic circuits; counting problems; polynomials

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Hervé Fournier, Guillaume Malod, Stefan Mengel. Monomials in arithmetic circuits: Complete problems in the counting hierarchy. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.362-373. ⟨hal-00678195⟩