Now showing 1 - 10 of 10
PublicationSome Undecidable Implication Problems for Path Constraints(1997-04-01) Buneman, Peter; Weinstein, Scott; Weinstein, ScottWe present a class of path constraints of interest in connection with both structured and semi-structured databases, and investigate their associated implication problems. These path constraints are capable of expressing natural integrity constraints that are not only a fundamental part of the semantics of the data, but are also important in query optimization. We show that, despite the simple syntax of the constraints, the implication problem for the constraints is r.e. complete and the finite implication problem for the constraints is co-r.e. complete. Indeed, we establish the existence of a conservative reduction of the set of all first-order sentences to the path constraint language. PublicationAlgorithmic Analysis of Array-Accessing Programs(2008-12-03) Alur, Rajeev; Weinstein, Scott; Cerný, Pavol; Weinstein, ScottFor programs whose data variables range over Boolean or finite domains, program verification is decidable, and this forms the basis of recent tools for software model checking. In this paper, we consider algorithmic verification of programs that use Boolean variables, and in addition, access a single array whose length is potentially unbounded, and whose elements range over pairs from Σ × D, where Σ is a finite alphabet and D is a potentially unbounded data domain. We show that the reachability problem, while undecidable in general, is (1) Pspace-complete for programs in which the array-accessing for-loops are not nested, (2) solvable in Ex-pspace for programs with arbitrarily nested loops if array elements range over a finite data domain, and (3) decidable for a restricted class of programs with doubly-nested loops. The third result establishes connections to automata and logics defining languages over data words. PublicationPath Constraints on Deterministic Graphs(1998-09-01) Buneman, Peter; Weinstein, Scott; Weinstein, ScottPath constraints have been studied in [4, 10, 11] for semistructured data modeled as a rooted edge-labeled directed graph. They have proven useful in the optimization of path queries. However, in this graph model, the implication problems associated with many natural path constraints are undecidable . A variant of the graph model, called the deterministic data model, was recently proposed in . In this model, data is represented as a graph with deterministic edge relations, i.e, the edges emanating from any node in the graph have distinct labels. The deterministic graph model is more appropriate for representing, for example, ACeDB  databases and Web pages. This paper investigates path constraints for the deterministic data model. It demonstrates the application of path constraints to, among other things, query optimization. Four classes of path constraints are considered: the class of word constraints Pw proposed in , the constraint language Pc introduced in , an extension of Pc, denoted by Pc-, by including wild cards in path expressions, and a generalization of Pc-, denoted by Pc*, by representing paths as regular expressions. The implication problems for these constraint languages are studied in the context of the deterministic data model. It shows that the implication and finite implication problems for Pw are decidable in cubic-time and are finitely axiomatizable. Moreover, in contrast to the undecidability result of , these results also hold for Pc. In addition the implication problems are decidable for Pc-. However, the implication problems for Pc* are undecidable. PublicationUniform Inductive Improvement(1989-05-11) Osherson, Daniel N; Weinstein, Scott; Weinstein, ScottWe examine uniform procedures for improving the scientific competence of inductive inference machines. Formally, such procedures are construed as recursive operators. Several senses of improvement are considered, including (a) enlarging the class of functions on which success is certain, and (b) transforming probable success into certain success. PublicationCentering: A Framework for Modelling the Local Coherence of Discourse(1995) Joshi, Aravind K.; Grosz, Barbara J.; Weinstein, Scott; Joshi, Aravind K.; Weinstein, ScottThis paper concerns relationships among focus of attention, choice of referring expression, and perceived coherence of utterances within a discourse segment. It presents a framework and initial theory of centering which are intended to model the local component of attentional state. The paper examines interactions between local coherence and choice of referring expressions; it argues that differences in coherence correspond in part to the inference demands made by different types of referring expressions given a particular attentional state. It demonstrates that the attentional state properties modelled by centering can account for these differences. PublicationFirst Order Logic, Fixed Point Logic and Linear Order(1995-11-01) Dawar, Anuj; Weinstein, Scott; Weinstein, ScottThe Ordered conjecture of Kolaitis and Vardi asks whether fixed-point logic differs from first-order logic on every infinite class of finite ordered structures. In this paper, we develop the tool of bounded variable element types, and illustrate its application to this and the original conjectures of McColm, which arose from the study of inductive definability and infinitary logic on proficient classes of finite structures (those admitting an unbounded induction). In particular, for a class of finite structures, we introduce a compactness notion which yields a new proof of a ramified version of McColm's second conjecture. Furthermore, we show a connection between a model-theoretic preservation property and the Ordered Conjecture, allowing us to prove it for classes of strings (colored orderings). We also elaborate on complexity-theoretic implications of this line of research. PublicationPath Constraints in the Presence of Types(1997-10-01) Buneman, Peter; Weinstein, Scott; Weinstein, ScottPath constraints have been studied in [3, 8, 9] for semi-structured data. In this paper, we investigate path constraints for structured data. We show that there is interaction between path constraints and type constraints. In other words, results on path constraint implication in semistructured databases may no longer hold in the presence of types. We also investigate the class of word constraints for databases of two practical object-oriented data models. In particular, we present an abstraction of the databases in these models in terms of first-order logic, and establish the decidability of word constraint implication in these models. PublicationThe Decidability of Some Restricted Implication Problems for Path Constraints(1997-05-01) Buneman, Peter; Weinstein, Scott; Weinstein, ScottIn , we introduced a path constraint language and established the undecidability of its associated implication problems. In this paper, we identify several fragments of the language, and establish the decidability of the implication and finite implication problems for each of these fragments in the context of semistructured databases. In addition, we demonstrate that these fragments suffice to express important semantic information such as extent constraint, inverse relationships and local database constraints commonly found in object-oriented databases. We also show that these fragments are useful for, among other things, query optimization. Publication*k*-Universal Finite Graphs(1996-02-01) Rosen, Eric; Weinstein, Scott; Weinstein, ScottThis paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah, establish that the class of k-universal graphs is not definable by an infinite disjunction of first-order existential sentences with a finite number of variables and that there exist k-universal graphs with no k-extendible induced subgraphs. PublicationPreservation Theorems in Finite Model Theory(1995-03-01) Weinstein, Scott; Weinstein, ScottWe develop various aspects of the finite model theory of Lk(there exists) and Lk∞omega(there exists). We establish the optimality of normal forms for Lk∞omega(there exists) over the class of finite structures and demonstrate separations over the class of finite structures and demonstrate separations among descriptive complexity classes within Lk∞omega(there exists). We establish negative results concerning preservation theorems for Lk(there exists) an Lk∞omega(there exists). We introduce a generalized notion of preservation theorem and establish some positive results concerning "generalized preservation theorems" for first-order definable classes of finite structures which are closed under extensions.