Independence of Containing Patterns Property and its Application in Tree Pattern Query Rewriting Using Views

Abstract We show that several classes of tree patterns observe the independence of containing patterns property, that is, if a pattern is contained in the union of several patterns, then it is contained in one of them. We apply this property to two related problems on tree pattern rewriting using views. First, given view V and query Q, is it possible for Q to have an equivalent rewriting using V which is the union of two or more tree patterns, but not an equivalent rewriting which is a single pattern? This problem is of both theoretical and practical importance because, if the answer is no, then, to find an equivalent rewriting of a tree pattern using a view, we should use more efficient methods, such as the polynomial time algorithm o

Negative boolean constraints

AbstractSystems of Boolean constraints which allow negative constraints such as f ⊊︀ g are investigated. The results form a basis for algorithms to determine satisfiability, validity, implication, equivalence and variable elimination for such systems. These algorithms have applications in spatial query decomposition, machine reasoning and constraint logic programming. Proofs of the results rely on independence of inequations, which enables results for systems with a single inequation to be lifted to systems with many inequations

Theories with the independence property

A first-order theory T has the Independence Property provided T ⊢ (Q)(Φ⇒

On Fourier's Algorithm for Linear Arithmetic

In the 1820's Fourier provided the first algorithm for solving linear arithmetic constraints. In other words, this algorithm determines whether or not the polyhedral set associated with the constraints is empty. We show here that Fourier's algorithm has an important hidden property: in effect it also computes the affine hull of the polyhedral set. This result is established by making use of a recent theorem on the independence of negative constraints

Chasing Constrained Tuple-Generating Dependencies

We investigate the implication problem for constrained tuple-generating dependencies (CTGDs), the extension of tuple- and equality-generating dependencies that permits expression of semantic relations (constraints) on variables. The implication problem is central to identifying redundant integrity constraints, checking integrity constraints on constraint databases, detecting independence of queries and updates, and optimizing queries. We provide two chase procedures for the implication problem. The first is cautious, generating tuples and constraints only when justified, whereas the second is speculative, generating tuples and constraints that have attached conditions about when they exist/hold. The cautious chase is more efficient, in some sense, but less powerful in demonstrating that a CTGD is implied. We demonstrate that, for constraint domains with Independence of Negative Constraints, the two chase procedures are equally powerful. The cautious chase is thus the chase of choice fo..