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For a problem of interval search on the Boolean cube, we study the asymptotic behaviour of the average search time in the class of balanced tree circuits on sequences of positive integers { k i   } under the assumption that  k i   are cardinalities of databases. We show that the asymptotic behaviour may differ on different sequences. We give a complete description of the class of possible behaviours.

The asymptotic behaviour of the complexity of the interval search on the Boolean cube in the class of balanced trees