We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation. This proves that the fixed point query hierarchy suggested by Chandra and Harel collapses at the first fixed point level. It is also a general result showing that in finite model theory one application of fixed point suffices. Introduction and Summary Query languages for relational databases have received considerable attention. In 1972 Codd showed that two natural languages for queries -- one algebraic and the other a version of first order predicate calculus -- have identical powers of expressibility, [Cod72]. Query languages which are as expressive as Codd's Relational Calculus are sometimes called complete. This term is misleading however becau...

This paper is an attempt at laying the foundations for the classification of queries on relational data bases according to their structure and their computational complexity. Using the operations of composition and fixpoints, a Z--// hierarchy of height w 2, called the fixpoint query hierarchy, is defined, and its properties investigated. The hierarchy includes most of the queries considered in the literathre including those of Codd and Aho and Ullman

We study two important extensions of first-order logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtained using a powerful normal form for while which shows that each while computation over an unordered domain can be reduced to a while computation over an ordered domain via a fixpoint query. The fixpoint query computes an equivalence relation on tuples which is a congruence with respect to the rest of the computation. The same technique is used to show that equivalence of tuples and structures with respect to FO formulas with bounded number of variables is definable in fixpoint. Generalizing fixpoint and while, we consider more powerful languages which model arbitrary computation interacting with a database using a finite set of FO queries. Such computation is modeled by a relational machine...

The set-height of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T,anintermediate type is a type which is used by some variable of the query, but which is not present in D or T.Foreachk, i ≥ 0 we define CALCk,i to be the family of calculus queries mapping from and to types with set-height ≤ k and using intermediate types with set-height ≤ i. In particular, CALC0,0 is the classical relational calculus, and CALC0,1 is equivalent to the family of secondorder (relational) queries. Several results concerning these families of languages are obtained. A primary focus is on the families CALC0,i, which map relations to relations. Upper and lower bounds in terms of hyper-exponential time and space on the complexity of these families are provided. The CALC0,i hierarchy does not collapse with respect to expressive power. The union ∪0≤iCALC0,i is exactly the family of elementary queries, i.e., queries with hyper-exponential complexity. The expressive power of queries from the complex object calculus interpreted using semantics based on the use of arbitrarily large finite or infinite set of invented values is studied. Under these semantics, the expressive power of the relational calculus is not increased, and the CALC0,i hierarchy collapses at CALC0,1. In general, queries with these semantics may not be computable. We also consider an alternative semantics which yields a family of queries equivalent to the computable queries. 1

In this paper we characterise exactly the complexity of a set based database language called SRL, which presents a unified framework for queries and updates. By imposing simple syntactic restrictions on it, we are able to express exactly the classes, P and LOGSPACE. We also discuss the role of ordering in database query languages and show that the hom operator of Machiavelli language in [OBB89] does not capture all the order-independent properties.

A formal framework is introduced for studying the semantics and expressiveness of active databases. The power of various abstract trigger languages is characterized, and related to several major active database prototypes such as ARDL, HiPAC, Postgres, Starburst, and Sybase. This allows to formally compare the expressiveness of the prototypes. The results provide insight into the programming paradigm of active databases, the interplay of various features, and their impact on expressiveness and complexity.

In recent years, several attempts have been made to define query... This paper describes the architecture and the implementation of a graphical query system, based on the diagrammatic representation of entity relationship schemata. The query language underlying the system allows the formulation of recursive queries; moreover, user interaction in both managing diagrams and expressing queries is simplified by the presence of a fully visual environment and a rich set of interaction strategies.

We present a language for querying list-based complex objects. The language is shown to express precisely the polynomial-time generic list-object functions. The iteration mechanism of the language is based on a new approach wherein, in addition to the list over which the iteration is performed, a second list is used to control the number of iteration steps. During the iteration, the intermediate results can be moved to the output list as well as re-inserted into the list being iterated over. A simple syntactic constraint allows the growth rate of the intermediate results to be tightly controlled which, in turn, restricts the expressiveness of the language to PTIME. Data Parallel Systems Inc., 4617 Morningside Dr., Bloomington, IN, 47408; email: colby@dpsi.com y University of Regina, Dept. of Comp. Science, Regina, Saskatchewan S4S 0A2, Canada, email: saxton@cs.uregina.ca z Indiana University, Comp. Science Dept., Bloomington, IN 47405-4101, email: vgucht@cs.indiana.edu. 1 Intro...

Visual Query Systems (VQS) are query systems using visual representations to denote the domain of interest and express related requests; they may be seen as an evolution of query languages adopted in database management systems. VQS are investigated to solve present day problems of conventional query systems. The most significant needs are: to provide a friendly man-machine interaction, to allow database search by non-technical users, to introduce a mechanism for comfortable navigation even in cases of incomplete and ambiguous queries. In order to explain, compare and evaluate the different features of the existing and suggested VQS, a taxonomy is proposed, based on expressive power, usability and classes of potential users. To clarify some taxonomic criteria, examples of representative VQS are given. 1. INTRODUCTION Many studies have been performed to improve man-machine interaction for allowing fruitful and friendly use of complex programs. Traditionally, in order to teach what speci...

This paper introduces a reflective extension of the relational algebra. Reflection is achieved by storing and manipulating relational algebra programs as relations and by adding a LISP-like evaluation operation to the algebra. We first show that this extension, which we call the reflective algebra, can serve as a unifying formalization of various forms of procedural data management which have been considered in database systems research. We then study the expressive power and complexity of the reflective algebra. In particular, we establish a close correspondence between reflection and bounded looping, and between tail-recursive reflection and unbounded looping. These correspondences yield new logical characterizations of PTIME and PSPACE. A preliminary version of this paper was presented at the Twelfth ACM Symposium on Principles of Database Systems (Washington, DC, May 1993). y Research Assistant of the Belgian National Fund for Scientific Research (NFWO). Address: Depa...