gyssensQcharlie.luc.ac.be laksQcs.concordia.ca We present a multi-dimensional database model, which we believe can serve as a con-ceptual model for On-Line Analytical Pro-cessing (OLAP)-based applications. Apart from providing the functionalities necessary for OLAP-based applications, the main fea-ture of the model we propose is a clear sepa-ration between structural aspects and the con-tents. This separation of concerns allows us to define data manipulation languages in a rea-sonably simple, transparent way. In particu-lar, we show that the data cube operator can be expressed easily. Concretely, we define an algebra and a calculus and show them to be equivalent. We conclude by comparing our ap-proach to related work. The conceptual multi-dimensional database model developed here is orthogonal to its im-plementation, which is not a subject of the present paper. 1

: We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. We formally define these notions and introduce the concept of query which generalizes queries over classical relational databases. We prove that in this context the basic properties of queries (satisfiability, containment, equivalence, etc.) are nonrecursive. We investigate the theory of finitely representable models and prove that it differs strongly from both classical model theory and finite model theory. In particular, we show that most of the well known theorems of either one fail (compactness, completeness, locality, 0/1 laws, etc.). An immediate consequence is the lack of tools to consider the definability of queries in the relational calculus over finitely representable databases. We illustrate this very challenging problem through some classical examples. We then mainly concentrate on dense order databases, and exhibit...

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Abstract We give an axiomatic description of parallel, synchronous algorithms. Our main result is that every such algorithm can be simulated, step for step, by an abstract state machine with a background that provides for multisets. \Lambda

Motivated by formal models recently proposed in the context of XML, we study automata and logics on strings over infinite alphabets. These are conservative extensions of classical automata and logics defining the regular languages on finite alphabets. Specifically, we consider register and pebble automata, and extensions of first-order logic and monadic second-order logic. For each type of automaton we consider one-way and two-way variants, as well as deterministic, nondeterministic, and alternating control. We investigate the expressiveness and complexity of the automata, their connection to the logics, as well as standard decision problems. Some of our results answer open questions of Kaminski and Francez on register automata.

We study definability problems and algorithmic issues for infinite structures that are finitely presented. After a brief overview over different classes of finitely presentable structures, we focus on structures presented by automata or by model-theoretic interpretations.

In this paper, we study the expressive power and the complexity of first-order logic with arithmetic, as a query language over relational and constraint databases. We consider constraints over various domains (N, Z, Q, and R), and with various arithmetical operations (6, +, \Theta, etc.). We first consider the data complexity of first-order queries. We prove in particular that linear queries can be evaluated in AC 0 over finite integer databases, and in NC 1 over linear constraint databases. This improves previously known bounds. We also show that over all domains, enough arithmetic lead to arithmetical queries, therefore, showing the frontiers of constraints for database purposes. We then tackle the problem of the expressive power, with the definability of the parity and the connectivity, which are the most classical examples of queries not expressible in first-order logic over finite structures. We prove that these two queries are first-order definable in presence of (enough) ari...

We present a logical approach to complexity over the real numbers with respect to the model of Blum, Shub and Smale. The logics under consideration are interpreted over a special class of two-sorted structures, called R-structures: They consist of a finite structure together with the ordered field of reals and a finite set of functions from the finite structure into R. They are a special case of the metafinite structures introduced recently by Grädel and Gurevich. We argue that R-structures provide the right class of structures to develop a descriptive complexity theory over R. We substantiate this claim by a number of results that relate logical definability on R-structures with complexity of computations of BSS-machines.

This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to game-based evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the

We rework parts of the classical relational theory when the underlying domain is a structure with some interpreted operations that can be used in queries. We identify parts of the classical theory that go through `as before' when interpreted structure is present, parts that go through only for classes of nicely-behaved structures, and parts that only arise in the interpreted case. The first category includes a number of results on language equivalence and expressive power characterizations for the active-domain semantics for a variety of logics. Under this semantics, quantifiers range over elements of a relational database. The main kind of results we prove here are generic collapse results: for generic queries, adding operations beyond order, does not give us extra power. The second category includes results on the natural semantics, under which quantifiers range over the entire interpreted structure. We prove, for a variety of structures, natural-active collapse results, s...