Equivalences among Relational Expressions

A. V. Aho, Y. Sagiv, J. D. Ullman
1979 SIAM journal on computing (Print)  
Many database queries can be formulated in terms of expressions whose operands represent tables of information (relations) and whose operators are the relational operations select, project, and join. This paper studies the equivalence problem for these relational expressions, with expression optimization in mind. A matrix, called a tableau, is proposed as a natural representative for the value of an expression. It is shown how tableaux can be made to reflect functional dependencies among
more » ... tes. A polynomial time algorithm is presented for the equivalence of tableaux that correspond to an important subset of expressions, although the equivalence problem is shown to be NP-complete under slightly more general circumstances. Next we introduce "simple tableaux," a subclass of tableau for which we can show the equivalence and optimization problems that were computationally difficult for general tableaux are now tractable. Although the set of queries having simple tableaux
doi:10.1137/0208017 fatcat:emu2qnlc7vazfjyrserdevjcxm