Seeking a manageable subclass of conjunctive queries over trees that would reach beyond tree patterns, we find that vertical acyclicity of queries is sufficient to guarantee the same complexity bounds for static analysis problems, as those enjoyed by tree patterns.

In a seminal contribution, Hansson (1976) demonstrates that the collection of decisive coalitions associated with an Arrovian social welfare function forms an ultrafilter. He goes on to show that if transitivity is weakened to quasi-transitivity as the coherence property imposed on a social relation, the set of decisive coalitions is a filter. We examine the notion of decisiveness with acyclica...

In this paper a proof of Conjecture 9.12 of Braverman–Kazhdan in their article γ-functions of representations and lifting on the acyclicity of their l-adic γ-sheaves over certain affine spaces is given for GL(n).

Existential rules, i.e. Datalog extended with existential quantifiers in rule heads, are currently studied under a variety of names such as Datalog+/–, ∀∃rules, and tuple-generating dependencies. The renewed interest in this formalism is fuelled by a wealth of recently discovered language fragments for which query answering is decidable. This paper extends and consolidates two of the main appro...

Suppose a strict preference relation fails to possess maximal elements, so that a choice is not clearly defined. I propose to delete particular instances of strict preferences until the resulting relation satisfies one of a number of known regularity properties (transitivity, acyclicity, or negative transitivity), and to unify the choices generated by different orders of deletion. Removal of st...

We propose new local move operators incorporated into a score-based stochastic greedy search algorithm to efficiently escape from local optima in the search space of directed acyclic graphs. We extend the classical set of arc addition, deletion, and reversal operators with a new operator replacing or swapping one parent to another for a given node, i.e. combining two elementary operations (arc ...

We present a dynamic data structure that keeps track of an acyclic hypergraph (equivalently, a triangulated graph) and enables verifying that adding a candidate hyperedge (clique) will not break the acyclicity of the augmented hypergraph. This is a generalization of the use of Tarjan’s Union-Find data structure for maintaining acyclicity when augmenting forests, and the amortized time per opera...