On satisfiability, equivalence, and implication problems involving conjunctive queries in database systems

Satisfiability, equivalence, and implication problems involving conjunctive queries are important and widely encountered problems in database management systems. These problems need to be efficiently and effectively solved. In this paper, we consider queries which are conjunctions of the inequalitie...

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Bibliographic Details
Published in:IEEE transactions on knowledge and data engineering Vol. 8; no. 4; pp. 604 - 616
Main Authors: Sha Guo, Wei Sun, Weiss, M.A.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.1996
IEEE Computer Society
Subjects:
Application software
Applied sciences
Arithmetic
Computer science; control theory; systems
Cost function
Database systems
Deductive databases
Distributed databases
Electrical capacitance tomography
Exact sciences and technology
Information systems. Data bases
Memory organisation. Data processing
Relational databases
Software
Sufficient conditions
Deductive database
Equivalence
Database query
Necessary and sufficient condition
NP hard problem
Database
Problem solving
Database management system
ISSN:1041-4347
Online Access:Get full text
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Summary:Satisfiability, equivalence, and implication problems involving conjunctive queries are important and widely encountered problems in database management systems. These problems need to be efficiently and effectively solved. In this paper, we consider queries which are conjunctions of the inequalities of the form (X op C), (X op Y), and/or (X op Y+C), where X and Y are two attributes, C is a constant, and op /spl epsiv/ {<, /spl les/, =,/spl ne/, >, /spl ges/}. These types of inequalities are widely used in database systems, since the first type is a selection, the second type is a /spl theta/-join, and the third type is a very popular clause in a deductive database system. The satisfiability, equivalence, and implication problems in the integer domain (for attributes and constants) have been shown to be NP-hard. However, we show that these problems can be solved efficiently in the real domain. The incorporation of the real domain is significant, because the real domain is practically and widely used in a database. Necessary and sufficient conditions and algorithms are presented. A novel concept of the "module closure" and a set of sound and complete axioms with respect to the "module closure" are also proposed to infer all correct and necessary inequalities from a given query. The proposed axioms generalize Ullman's axioms (1989) where queries only consist of /spl theta/-joins.
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ISSN:1041-4347
DOI:10.1109/69.536253