Correct algebras over estimation algorithms in the set of regular recognition problems with nonoverlapping classes
We investigate the succinctness problem for conjunctive query rewritings over OWL 2QL ontologies of depth 1 and 2 by means of hypergraph programs computing Boolean functions. Both positive and negative results are obtained. We show that, over ontologies of depth 1, conjunctive queries have polynomial-size nonrecursive datalog rewritings; tree-shaped queries have polynomial positive existential rewritings; however, in the worst case, positive existential rewritings can be superpolynomial. Over ontologies of depth 2, positive existential and nonrecursive datalog rewritings of conjunctive queries can suffer an exponential blowup, while first-order rewritings can be superpolynomial unless NP ⊆ P/poly. We also analyse rewritings of tree-shaped queries over arbitrary ontologies and note that query entailment for such queries is fixed-parameter tractable.
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This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
We give solutions to two fundamental computational problems in ontology-based data access with the W3C standard ontology language OWL 2 QL: the succinctness problem for first-order rewritings of ontology-mediated queries (OMQs) and the complexity problem for OMQ answering. We classify OMQs according to the shape of their conjunctive queries (treewidth, the number of leaves) and the existential depth of their ontologies. For each of these classes, we determine the combined complexity of OMQ answering and whether all OMQs in the class have polynomial-size first-order, positive existential, and nonrecursive datalog rewritings. We obtain the succinctness results using hypergraph programs, a new computational model for Boolean functions, which makes it possible to connect the size of OMQ rewritings and circuit complexity.
A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.