We study the complexity of the problem of answering queries using materialized views. This problem has attracted a lot of attention recently because of its relevance in data integration. Previous work considered only conjunctive view definitions. We examine the consequences of allowing more expressive view definition languages. The languageswe consider for view definitions and user queries are: conjunctive queries with inequality, positive queries, datalog, and first-order logic. We show that the complexity of the problem depends on whether views are assumed to store all the tuples that satisfy the view definition, or only a subset of it. Finally, we apply the results to the view consistency and view self-maintainability problems which arise in data warehousing. 1 Introduction The notion of materialized view is essential in databases [34] and is attracting more and more attention with the popularity of data warehouses [28]. The problem of answering queries using materialized views [24...

A drawback which concept languages based on kl-one have is that all the terminological knowledge has to be defined on an abstract logical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defining concepts. Examples for such concrete domains are the integers, the real numbers, or also non-arithmetic domains, and predicates could be equality, inequality, or more complex predicates. In the present paper we shall propose a scheme for integrating such concrete domains into concept languages rather than describing a particular extension by some specific concrete domain. We shall define a terminological and an assertional language, and consider the important inference problems such as subsumption, instantiation, and consistency. The formal semantics as well as the reasoning algorithms are given on the scheme level. In contrast to existing kl-one based systems, these algorithms will be not only sound but also complete. The...

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The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NP-completeness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, time-varying linear systems, nonlinear and hybrid systems, and stochastic optimal control.

This paper is concerned with the model for security of cryptographic protocols suggested by Dolev and Yao. The Dolev and Yao model deals with a restricted class of protocols, known as Two-Party Ping-Pong Protocols. In such a protocol, messages are exchanged in a memoryless manner. That is, the message sent by each party results from applying a predetermined operator to the message he has received. The Dolev and Yao model is presented, generalized in various directions and the affect of these generalizations is extensively studied. First, the model is trivially generalized to deal with multi-party ping-pong protocols. However, the problems which arise from this generalization are very far from being trivial. In particular, it is no longer clear how many saboteurs (adversaries) should be considered when testing the security of p-party ping-pong protocols. We demonstrate an upper bound of 3(p \Gamma 2) + 2 and a lower bound of 3(p \Gamma 2) + 1 on this number. Thus, for every fixed p, th...

We formalize the Dolev-Yao model of security protocols, using a notation based on multi-set rewriting with existentials. The goals are to provide a simple formal notation for describing security protocols, to formalize the assumptions of the Dolev-Yao model using this notation, and to analyze the complexity of the secrecy problem under various restrictions. We prove that, even for the case where we restrict the size of messages and the depth of message encryption, the secrecy problem is undecidable for the case of an unrestricted number of protocol roles and an unbounded number of new nonces. We also identify several decidable classes, including a dexp-complete class when the number of nonces is restricted, and an np-complete class when both the number of nonces and the number of roles is restricted. We point out a remaining open complexity problem, and discuss the implications these results have on the general topic of protocol analysis.

This paper presents a method for reasoning about spatial objects and their qualitative spatial relationships. In contrast to existing work, which mainly focusses on reasoning about qualitative spatial relations alone, we integrate quantitative and qualitative information with terminological reasoning. For spatioterminological reasoning we present the description logic ALCRP(D) and define an appropriate concrete domain D for polygons. The theory is motivated as a basis for knowledge representation and query processing in the domain of deductive geographic information systems. 1 Introduction Qualitative relations play an important role in formal reasoning systems that can be part of, for instance, geographic information systems (GIS). In this context, inferences about spatial relations should not be considered in isolation but should be integrated with formal inferences about structural descriptions of domain objects (e.g. automatic consistency checking and classification) and infer...

this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction

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We prove that several problems associated to probabilistic finite automata are undecidable for automata whose number of input letters and number of states are fixed. As a corollary of one of our results we prove that the problem of determining if the set of all products of two 47 × 47 matrices with nonnegative rational entries is bounded is undecidable.