@inbook {IOPORT.06070916, author = {Fournier, Herv\'e and Malod, Guillaume and Mengel, Stefan}, title = {Monomials in arithmetic circuits: complete problems in the counting hierarchy.}, year = {2012}, booktitle = {STACS 2012. 29th international symposium on theoretical aspects of computer science, Paris, France, February 29th -- March 3rd, 2012}, isbn = {978-3-939897-35-4}, pages = {362-373, electronic only}, publisher = {Wadern: Schloss Dagstuhl -- Leibniz Zentrum f\"ur Informatik}, doi = {10.4230/LIPIcs.STACS.2012.362}, abstract = {Summary: 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.}, identifier = {06070916}, }