Conjunctive-query containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctive-query containment and constraint satisfaction have in common? Our main conceptual contribution in this paper is to point out that, despite their very different formulation, conjunctive-query containment and constraint satisfaction are essentially the same problem. The reason is that they can be recast as the following fundamental algebraic problem: given two finite relational structures A and B, is there a homomorphism h : A ! B? As formulated above, the homomorphism problem is uniform in the sense that both relational structures A and B are part of the input. By fixing the structure B, one obtains the following non-uniform problem: given a finite relational structure A, is there a homomorphism h : A ! B? In general, non-uniform tractability results do not uniformize. Thus, it is natural to ask: which tractable cases of non-uniform tractability results for constraint satisfaction and conjunctive-query containment do uniformize? Our main technical contribution in this paper is to show that several cases of tractable non-uniform constraint satisfaction problems do indeed uniformize. We exhibit three non-uniform tractability results that uniformize and, thus, give rise to polynomial-time solvable cases of constraint satisfaction and conjunctive-query containment.

The expressive power of first-order query languages with several classes of equality and inequality constraints is studied in this paper. We settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomial inequality constraints over the reals. Furthermore, noting that relational queries exhibit several forms of genericity, we establish a number of collapse results of the following form: The class of generic boolean queries expressible in the relational calculus augmented with a given class of constraints coincides with the class of queries expressible in the relational calculus (with or without an order relation). We prove such results for both the natural and active-domain semantics. As a consequence, the relational calculus augmented with polynomial inequalities expresses the same classes of generic boolean queries under both the natural and active-domain semantics. In the course of proving...

. We introduce the concept of a class of graphs being locally tree-decomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded tree-width. We show that for each locally tree-decomposable class C of graphs and for each property ' of graphs that is denable in rst-order logic, there is a linear time algorithm deciding whether a given graph G 2 C has property '. 1 Introduction It is an important task in the theory of algorithms to nd feasible instances of otherwise intractable algorithmic problems. A notion that has turned out to be extremely useful in this context is that of tree-width of a graph. 3-Colorability, Hamiltonicity, and many other NP-complete properties of graphs can be decided in linear time when restricted to graphs whose tree-width is bounded by a xed constant (see [Bod97] for a survey). Courcelle [Cou90] proved a meta-theorem, which easily implies numer...

. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional -calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the -calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the -calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...

We study here the language Datalog(6=), which is the query language obtained from Datalog by allowing equalities and inequalities in the bodies of the rules. We view Datalog(6=) as a fragment of an innitary logic L ! and show that L ! can be characterized in terms of certain two-person pebble games. This characterization provides us with tools for investigating the expressive power of Datalog(6=). As a case study, we classify the expressibility of fixed subgraph homeomorphism queries on directed graphs. Fortune et al. [FHW80] classied the computational complexity of these queries by establishing two dichotomies, which are proper only if P 6= NP. Without using any complexity-theoretic assumptions, we show here that the two dichotomies are indeed proper in terms of expressibility in Datalog(6=).

We investigate the in nitary logic L 1! , in which sentences may have arbitrary disjunctions and conjunctions, but they involve only a nite number of distinct variables. We show that various xpoint logics can be viewed as fragments of L 1! , and we describe a game-theoretic characterization of the expressive power of the logic. Finally, we study asymptotic probabilities of properties 1! on nite structures. We show that the 0-1 law holds for L 1! , i.e., the asymptotic probability of every sentence in this logic exists and is equal to either 0 or 1. This result subsumes earlier work on asymptotic probabilities for various xpoint logics and reveals the boundary of 0-1 laws for in nitary logics.

We provide new techniques for the analysis of the expressive power of query languages for nested collections. These languages may use set or bag semantics and may be further complicated by the presence of aggregate functions. We exhibit certain classes of graphs and prove that the properties of these graphs that can be tested in such languages are either finite or cofinite. This result settles the conjectures of Grumbach, Milo, and Paredaens that parity test, transitive closure, and balanced binary tree test are not expressible in bag languages like the PTIME fragment of BALG of Grumbach and Milo and BQL of Libkin and Wong. Moreover, it implies that many recursive queries, including simple ones like the test for a chain, cannot be expressed in a nested relational language even when aggregate functions are available. In an attempt to generalize the finite-cofiniteness result, we study the bounded degree property which says that the number of distinct in- and out-degrees in the output of...

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. Expressiveness of database query languages remains the major motivation for research in finite model theory. However, most techniques in finite model theory are based on Ehrenfeucht-Fraisse games, whose application often involves a rather intricate argument. Furthermore, most tools apply to first-order logic and some of its extensions, but not to languages that resemble real query languages, like SQL. In this paper we use locality to analyze expressiveness of query languages. A query is local if, to determine if a tuple belongs to the output, one only has to look at a certain predetermined portion of the input. We study local properties of queries in a context that goes beyond the pure first-order case, and then apply the resulting tools to analyze expressive power of SQL-like languages. We first prove a general result describing outputs of local queries, that leads to many easy inexpressibility proofs. We then consider a closely related bounded degree property, which d...

Tree-walking automata (TWAs) recently received new attention in the fields of formal languages and databases. Towards a better understanding of their expressiveness, we characterize them in terms of transitive closure logic formulas in normal form. It is conjectured by Engelfriet and Hoogeboom that TWAs cannot de ne all regular tree languages, or equivalently, all of monadic second-order logic. We proof this conjecture for a restricted, but powerful, class of TWAs. In particular, we show that 1-bounded TWAs, that is TWAs that are only allowed to traverse every edge of the input tree at most once in every direction, cannot de ne all regular languages. We then extend this result to a class of TWAs that can simulate first-order logic (FO) and is capable of expressing properties not definable in FO extended with regular path expressions; the latter logic being avalid abstraction of current query languages for XML and semi-structured data.