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Regular nary queries in trees and variable independence
 in: International Conference on Theoretical Computer Science (IFIP TCS), 2008
"... Summary. Regular nary queries in trees are queries which are definable by an MSO formula with n free firstorder variables. We investigate the variable independence problem – originally introduced for databases – in the context of trees. In particular, we show how to decide whether a regular query ..."
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Summary. Regular nary queries in trees are queries which are definable by an MSO formula with n free firstorder variables. We investigate the variable independence problem – originally introduced for databases – in the context of trees. In particular, we show how to decide whether a regular query is equivalent to a union of cartesian products, independently of the input tree. As an intermediate step, we reduce this problem to the problem of deciding whether the number of answers to a regular query is bounded by some constant, independently of the input tree. As a (nontrivial) generalization, we introduce variable independence w.r.t. a dependence forest between blocks of variables, which we prove to be decidable. 1