Abstract: Methods and apparatus are provided for ensuring that queries presented to a database are safe thus providing solutions to both undecidability and lack of effective syntax issues. In a one aspect of the invention, a method for use in a database system includes obtaining an original query entered by a user. The invention then provides for pre-processing the query before submittal to a database engine associated with the database system wherein a result of the pre-processing operation is to ensure that a query provided to the engine is safe. Safety has a different meaning depending on the application. For example, safety may include ensuring that a query will return an output with finite results or it may include ensuring that certain geometric properties in the query are preserved in the output.

Abstract: A method and apparatus for querying a disjunctive database is disclosed. An annotated object, which defines a complete object which is a unique element of the normal form of the database, is stored and maintained in memory. A complete object is created using the annotated object, and is stored in memory. A query is run against the complete object. If continued processing is required, a next function produces a next annotated object, which represents another unique element of the normal form of the database. The next annotated object is stored in memory, overwriting the previous annotated object. A complete object is then created using the next annotated object and is stored in memory, overwriting the previous complete object. The query is then applied to the complete object stored in memory. By processing the elements of the normal form one at a time and reusing memory spaces, the present invention has a polynomial space requirement.

Abstract: Apparatus and methods for reducing the amount of computation required to determine the consequences of a side effect resulting from a transaction on a relation in a data base system. The apparatus and methods use equational reasoning based on a bag algebra representation of a class of transaction and the relation to produce a pre-expression which describes the side effect. The pre-expression is included in the data base system's data dictionary, and when a transaction of the class is received in the data base system, the pre-expression is used to determine the side effect. The pre-expression is formed with a strongly-minimal pair of delete and insert bags. The apparatus and methods may be used to maintain materialized views, to check for violation of constraints on the data base, and to activate triggers, monitors, and active queries.