Related papers: Decomposition by tree dimension in Horn clause ver…
In this paper, we show how the notion of tree dimension can be used in the verification of constrained Horn clauses (CHCs). The dimension of a tree is a numerical measure of its branching complexity and the concept here applies to Horn…
Developing an efficient non-linear Horn clause solver is a challenging task since the solver has to reason about the tree structures rather than the linear ones as in a linear solver. In this paper we propose an incremental approach to…
In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program…
Treewidth is a parameter that measures how tree-like a relational instance is, and whether it can reasonably be decomposed into a tree. Many computation tasks are known to be tractable on databases of small treewidth, but computing the…
A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization, i.e., a cycle-free realization of the code on the…
Treewidth is a graph parameter that plays a fundamental role in several structural and algorithmic results. We study the problem of decomposing a given graph $G$ into node-disjoint subgraphs, where each subgraph has sufficiently large…
This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously…
Programs that manipulate tree-shaped data structures often require complex, specialized proofs that are difficult to generalize and automate. This paper introduces a unified, foundational approach to verifying such programs. Central to our…
In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most its divisorial gonality. The proof gives a polynomial time algorithm to construct a tree decomposition of width at most $k$, when an effective…
We present a constraint model for the problem of producing a tree decomposition of a graph. The inputs to the model are a simple graph G, the number of nodes in the desired tree decomposition and the maximum cardinality of each node in that…
We here investigate on the complexity of computing the \emph{tree-length} and the \emph{tree-breadth} of any graph $G$, that are respectively the best possible upper-bounds on the diameter and the radius of the bags in a tree decomposition…
Verifying programs that manipulate tree data structures often requires complex, ad-hoc proofs that are hard to generalize and automate. This paper introduces an automatic technique for analyzing such programs. Our approach combines automata…
We introduce tree dimension and its leveled variant in order to measure the complexity of leaf sets in binary trees. We then provide a tight upper bound on the size of such sets using leveled tree dimension. This, in turn, implies both the…
This paper proposed an approach to automatically discovering subject dimension, action dimension, object dimension and adverbial dimension from texts to efficiently operate texts and support query in natural language. The high quality of…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
Tree-decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. The main property of tree-decompositions is the width (the maximum size of a bag minus 1). We show that every graph has a…
The notion of $\mathcal{H}$-treewidth, where $\mathcal{H}$ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of $\mathcal{H}$-treewidth at most $k$…
Tree-decompositions and treewidth are of fundamental importance in structural and algorithmic graph theory. The "spread" of a tree-decomposition is the minimum integer $s$ such that every vertex lies in at most $s$ bags. A…
We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or…
This paper presents a tree-to-tree transduction method for sentence compression. Our model is based on synchronous tree substitution grammar, a formalism that allows local distortion of the tree topology and can thus naturally capture…