\begin{abstract}
Given a monomial ideal $I=\angle{m_1,m_2,\cdots,m_k}$ where $m_i$
are monomials and a polynomial $f$ as an arithmetic circuit the
\emph{Ideal Membership Problem } is to test if $f\in I$. We study
this problem and show the following results.
\begin{itemize}
\item[(a)] If the ideal $I=\angle{m_1,m_2,\cdots,m_k}$ for a
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The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain characterizations for the single levels of these hierarchies and obtain the following results:

1. The classes of ... more >>>

The Counting Constraint Satisfaction Problem (#CSP(H)) over a finite
relational structure H can be expressed as follows: given a
relational structure G over the same vocabulary,
determine the number of homomorphisms from G to H.
In this paper we characterize relational structures H for which
#CSP(H) can be solved in ... more >>>