Monomials in arithmetic circuits: Complete problems in the counting hierarchy

Details Monomials in arithmetic circuits: Complete problems in the counting hierarchy Monomials in arithmetic circuits: Complete problems in the counting hierarchy

2011-10-28

arxiv.org/abs/1110.6271v2

Computer Science

Computational Complexity

Scientific paper

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. We
also study these questions for circuits computing multilinear polynomials.

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