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The Fixpoint BoundedVariable Queries are PSPACEComplete
 Presented at the 10th Annual International Conference of the European Association for Computer Science Logic, CSL '96
, 1996
"... We study complexity of the evaluation of fixpoint boundedvariable queries in relational databases. We exhibit a finite database such that the problem whether a closed fixpoint formula using only 2 individual variables is satisfied in this database is PSPACEcomplete. This clarifies the issues ra ..."
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We study complexity of the evaluation of fixpoint boundedvariable queries in relational databases. We exhibit a finite database such that the problem whether a closed fixpoint formula using only 2 individual variables is satisfied in this database is PSPACEcomplete. This clarifies the issues raised by Moshe Vardi in [Var95]. We study also the complexity of query evaluation for a number of restrictions of fixpoint logic. In particular we exhibit a sublogic for which the upper bound postulated by Vardi holds.
The Complexity of Computing the kary Composition of a Binary Associative Operator
, 1996
"... We show that the problem of computing all contiguous kary compositions of a sequence of n values under an associative and commutative operator requires 3 k\Gamma1 k+1 n \Gamma O(k) operations. For the operator max we show in contrast that in the decision tree model the complexity is i 1 + ..."
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We show that the problem of computing all contiguous kary compositions of a sequence of n values under an associative and commutative operator requires 3 k\Gamma1 k+1 n \Gamma O(k) operations. For the operator max we show in contrast that in the decision tree model the complexity is i 1 + \Theta(1= p k) j n \Gamma O(k). Finally we show that the complexity of the corresponding online problem for the operator max is i 2 \Gamma 1 k\Gamma1 j n \Gamma O(k). This work was partially supported by the ESPRIT Long Term Research Program of the EU under contract #20244 (ALCOMIT). y Supported by the Danish Natural Science Research Council (Grant No. 9400044). z Basic Research in Computer Science, Centre of the Danish National Research Foundation. 1 Introduction Given a sequence of values (x 1 ; x 2 ; : : : ; x n ) from a universe U and an associative binary operator \Phi, we consider the problem of computing all kary compositions of contiguous subsequences of length...