Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such properties is non-obvious and can be challenging indeed. In this paper, we take acyclicity properties into consideration and investigate logic-based approaches to encode them. We use answer set programming as the primary repre...

Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in multiprocessor scheduling. We identified the additional constraint of acyclic dependencies between blocks when mapping computer vision and imaging applications to a hete...

Programming languages with dynamic memory allocation, such as Java, allow creating and manipulating cyclic data structures. The presence of cyclic data structures in the program memory (the heap) is a challenging issue in the context of termination analysis [4, 5, 1, 14], resource usage analysis [15, 7, 2], garbage collection [11], etc. Consider the loop “while (x!=null) do x:=x.next;”. If x po...

We study the decision problem for the language DGRA (directed graphs with reachability and acyclicity), a quantifier-free fragment of graph theory involving the notions of reachability and acyclicity. We prove that the language DGRA is decidable, and that its decidability problem is NP -complete. We do so by showing that the language enjoys a small model property : If a formula is satisfiable, ...

Existential rules have been proposed for representing on-tological knowledge, specifically in the context of Ontology-BasedQuery Answering. Entailment with existential rules is undecidable.We focus in this paper on conditions that ensure the terminationof a breadth-first forward chaining algorithm known as the chase.First, we propose a new tool that allows to extend existing...