On PAC learnability of functional dependencies

Relational model is the most essential database model for decades and is examined in various ways. A very important concept in the relational modeling is the concept of dependencies. Particularly a set of functional dependencies and its equivalent minimal cover are discussed here for synthesizing third normal form relations. A traditional synthesis algorithm have been used to reduce the set of functional dependencies, F, into an equivalent minimal cover. This cover is then used to develop a relational schema; however, a given set of functional dependencies may have more than one minimal covers. In turn, different minimal covers may give rise to different relational schema. Database designers had already been agreed upon the use of popular inference rules of Armstrong to obtain minimal covers from the set F of functional dependencies. Despite the frequent use of the traditional synthesis algorithm, there is still a lack of formality and simplicity support in that algorithm to produce a minimum cover, especially; the step(s) of the algorithm in which the set of functional dependencies of F are used to make left-irreducible remain informal. In this paper, an extension is proposed to the synthesis algorithm that aids in to produce an optimal minimal cover more systematically from the given set of functional dependencies. The optimal minimal cover obtained by this extension would be appropriate for synthesizing third normal form relational schema from the universal relation scheme.

Characterizations for functional dependency and Boyce-Codd normal form families

In this paper, we consider functional dependencies among Boolean dependencies (BDs, for short). Armstrong relations are defined for BDs (called BD-Armstrong relations). For BDs, two necessary and sufficient conditions for the existence of BD-Armstrong relations are given. A necessary and sufficient condition for the existence of Armstrong relations for functional dependencies (FDs, for short) is given, which in some sense is more convenient than the condition given in [3]. We give an algorithm that solves the problem of deciding if two BDs imply the same set of functional dependencies. If the BDs are given in perfect disjunctive normal form, then the algorithm requires only polynomial time. Although Mannila and Raiha have shown that for some relations exponential time is needed for computing any cover of the set of FDs defined in this relation, as a consequence, we show that the problem of deciding if two relations satisfy the same set of FDs can be solved in polynomial time. Another consequence is a new correspondence of the families of functional dependencies to the families of Sperner systems. By this correspondence, the estimate of the number of databases given previously in [6] is improved. It is shown that there is a one-to-one correspondence between the closure of the FDs that hold in a BD and its so-calledbasic cover. As applications of basic covers, we obtain a representation of a key, the family of minimal keys and a representation of canonical covers.

On learning multivalued dependencies with queries

Let R be a γ-acyclic relational scheme, and let F be the set of functional dependencies (FD's) embodied in R. Given an existence constrained database r over R, it was shown in [1] that it is possible to connect tuples from different relations in r and construct a universal instance L, possibly containing null values δ, such that the total projection of L onto R yields exactly the set r. Moreover, conditions were given which guarantee that this L would satisfy the functional dependency with nulls (NFD) counterparts of FD's, in F. The purpose of this note is to generalize the latter result and show that under the same conditions, L actually satisfies NFD counterparts of FD's in the closure F+ of F.

Most algorithms in relational database theory use a set of functional dependencies as their input. The efficiency of the algorithms depends on the size of the set. The notions of a minimum set (with as few dependencies as possible) and an optimum set (which is as short as possible) were introduced by Maier. He showed that while a minimum cover for a given set of dependencies can be found in polynomial time, obtaining an optimum cover is an NP-complete problem. Here the relationship of these covers is explored further. It is shown that the length of a minimum set (i) cannot be bounded by a linear function on the length of an optimum cover, and (ii) is bounded by the square of the length of an optimum cover. It is also shown that the NP-completeness of the optimization problem is somewhat surprisingly caused solely by the difficulty of optimizing a single class of dependencies having equivalent left sides, not by the globality of the optimality condition. This result has some practical significance, since the equivalence classes appearing in practice are short. The problem of optimizing an equivalence class is studied and left and right sides of a dependency are shown to behave differently. A new representation for equivalence classes based on this observation is suggested. The optimization of single dependencies is shown to be NP-complete, and a method to produce good approximations is given.

In order to accurately identify Linear Parameter-Varying (LPV) systems, order selection of LPV linear regression models has prime importance. Existing identification approaches in this context suffer from the drawback that a set of functional dependencies needs to be chosen a priori for the parametrization of the model coefficients. However in a black-box setting, it has not been possible so far to decide which functions from a given set are required for the parametrization and which are not. To provide a practical solution, a nonnegative garrote approach is applied. It is shown that using only a measured data record of the plant, both the order selection and the selection of structural coefficient dependence can be solved by the proposed method.

It is well known that faithful (i.e. dependency preserving) decompositions of relational database schemas into Boyce-Codd Normal Form (BCNF) do not always exist, depending on the set of functional dependencies given, and that the corresponding decision problem is NP-hard. The only algorithm to guarantee both faithfulness and BCNF (if possible) proposed so far in [Os79] is a brute-force approach which always requires exponential time. To be useful in practice, e.g. in automated design tools, we require more efficient means.In this paper we present an algorithm which always finds a faithful BCNF decomposition if one exists, and which is usually efficient, and exponential only in notorious cases.

On completing tables to satisfy functional dependencies

Managing inconsistency in databases has long been recognized as an important problem. One of the most promising approaches to coping with inconsistency in databases is the framework of database repairs, which has been the topic of an extensive investigation over the past several years. Intuitively, a repair of an inconsistent database is a consistent database that differs from the given inconsistent database in a minimal way. So far, most of the work in this area has addressed the problem of obtaining the consistent answers to a query posed on an inconsistent database. Repair checking is the following decision problem: given two databases r and r′, is r′ a repair of r? Although repair checking is a fundamental algorithmic problem about inconsistent databases, it has not received as much attention as consistent query answering. In this paper, we give a polynomial-time algorithm for subset-repair checking under integrity constraints that are the union of a weakly acyclic set of local-as-view (LAV) tuple-generating dependencies and a set of equality-generating dependencies. This result significantly generalizes earlier work for subset-repair checking when the integrity constraints are the union of an acyclic set of inclusion dependencies and a set of functional dependencies. We also give a polynomial-time algorithm for symmetric-difference repair checking, when the integrity constraints form a weakly acyclic set of LAV tgds. After this, we establish a number of complexity-theoretic results that delineate the boundary between tractability and intractability for the repair-checking problem. Specifically, we show that the aforementioned tractability results are optimal; in particular, subset-repair checking for arbitrary weakly acyclic sets of tuple-generating dependencies is a coNP-complete problem. We also study cardinality-based repairs and show that cardinality-repair checking is coNP-complete for various classes of integrity constraints encountered in database design and data exchange. Copyright 2009 ACM.

A Combined Framework for Grouping and Order Optimization

Recently, with the rapid spread of computer technology, XML has become the standard for data exchange for a wide variety of applications. A large number of XML and XML schema are generated by different individual or company. The problem addressed in this paper is the execution of XML queries over multiple XML documents. In this paper, we propose an algorithm: SMXQA (semantics based multi-XML query algorithm). In the SMXQA, we parse the DTD/XSD of multi-XML documents to collect the set of functional dependency in it. Then we use method of clustering and pattern matching based on semantic to catch the element with homologous semantic in the set of functional dependency. And we concentrate on make a global materialized view by that element. For query conveniently, we propose a multi-XML query language: MXquery, which is extended from Xquery. At last, we experimentally evaluate the effectiveness of the proposed algorithm.

Normal forms and syntactic completeness proofs for functional independencies

In the present paper a distance concept of databases is investigated. Two database instances are of distance 0, if they have the same number of attributes and satisfy exactly the same set of functional dependencies. This naturally leads to the poset of closures as a model of changing database. The distance of two databases (closures) is defined to be the distance of the two closures in the Hasse diagram of that poset. We determine the diameter of the poset and show that the distance of two closures is equal to the natural lower bound, that is to the size of the symmetric difference of the collections of closed sets. We also investigate the diameter of the set of databases with a given system of keys. Sharp upper bounds are given in the case when the minimal keys are 2 (or r)-element sets.Keywordsdistance of databaseskeysantikeysclosuresposetHasse diagram

We investigate the probabilistic quantum cloning (PQC) of two states with arbitrary probability distribution. The optimal success probabilities are worked out for $$1\rightarrow 2$$1 2 PQC of the t...