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Computing queries from derived relations, optimizing queries from a group of queries, and updating materialized views are important database problems and have attracted much attention. One thing common to these problems is their demand to quickly solve the implication problem — given two predicates σ Q and σ τ , can σ Q imply σ τ (σ Q →σ τ )? The implication problem has been solved by converting it into a satisfiability problem. Based on a graph representation, a detailed study of the general implication problem on its own is presented in this paper. We proved that the general implication problem, in which all six comparison operators: =, ≠, <, >, ≤, ≥, as well as conjunctions and disjunctions are allowed, is NP-hard. In the case when “≠” operators are not allowed in σ Q and disjunctions are not allowed in σ τ , a polynomial time algorithm is proposed to solve this restricted implication problem. The influence of the “≠” operator and disjunctions are studied. Our theoretical results show that for some special cases the polynomial complexity algorithm can solve the implication problem which allows the “≠” operator or disjunctions in the predicates. Necessary conditions for detecting when the “≠” operator and disjunctions are allowed are also given. These results are very useful in creating heuristic methods.

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In this paper a new method to improve the utilization of main memory systems is presented. The new method is based on prestoring m main memory a number of query answers, each evaluated out of a single memory page. To this end, the ideas of page-answers and page-traces are formally described and their properties analyzed. The query model used here allows for selection, projection, join, recursive queries as well as arbitrary combinations. We also show how to apply the approach under update traffic. This concept is especially useful in managing the main memories of an important class of applications. This class includes the evaluation of triggers and alerters, performance improvement of rule-based systems, integrity constraint checking, and materialized views. These applications are characterized by the existence at compile time of a predetermined set of queries, by a slow but persistent update traffic, and by their need to repetitively reevaluate the query set. The new approach represents a new type of intelligent database caching, which contrasts with traditional caching primarily in that the cache elements are derived data and as a consequence, they overlap arbitrary and do not have a fixed length. The contents of the main memory cache are selected based on the data distribution within the database, the set of fixed queries to preprocess, and the paging characteristics Page-answers and page-traces are used as the smallest indivisible units in the cache. An efficient heuristic to select a near optimal set of page-answers and page-traces to populate the main memory has been developed. implemented, and tested. Finally, quantitative measurements of performance benefits are reported.

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Abstract. Several object-oriented database management systems have been implemented without an accompanying theoretical foundation for constraint, query specification, and processing. The pattern-based object calculus presented in this article provides such a theoretical foundation for describing and processing objectoriented databases. We view an object-oriented database as a network of interrelated classes (i.e., the intension) and a collection of time-varying object association patterns (i.e., the extension). The object calculus is based on first-order logic. It provides the formalism for interpreting precisely and unifor/nly the semantics of queries and integrity constraints in object-oriented databases. The power of the object calculus is shown in four aspects. First, associations among objects are expressed explicitly in an object-oriented database. Second, the "nonassociation" operator is included in the object calculus. Third, set-oriented operations can be performed on both homogeneous and heterogeneous object association patterns. Fourth, our approach does not assume a specific form of database schema. A proposed formalism is also applied to the design of high-level object-oriented query and constraint languages.