In this paper we explore the problem of counting solutions to conjunctive queries. We consider a parameter called the quantified star size of a formula Ï• which measures how the free variables areâ€¦ (More)

Decomposable Negation Normal Forms (DNNFs) are a restricted form of Boolean circuits in negation normal form where the subcircuits leading into each AND gate are defined on disjoint sets ofâ€¦ (More)

Choosing a language for knowledge representation and reasoning involves a trade-off between two competing desiderata: succinctness (the encoding should be small) and tractability (the language shouldâ€¦ (More)

Conjunctive queries are basic and heavily studied database queries; in relational algebra, they are the select-project-join queries. In this article, we study the fundamental problem of counting,â€¦ (More)

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 areâ€¦ (More)

We show that #SAT on Î²-acyclic CNF-formulas can be solved in polynomial time. In contrast to previous algorithms for other structurally restricted classes of formulas, our algorithm does not proceedâ€¦ (More)

This paper is a study of weighted counting of the solutions of acyclic conjunctive queries (ACQ). The unweighted quantifier free version of this problem is known to be tractable (for combinedâ€¦ (More)

We investigate the complexity of an optimization problem in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfyingâ€¦ (More)