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The history of schema languages for XML is an increase of expressiveness. While early schema languages mainly focused on the element structure, Clark first paid an equal attention to attributes by allowing both element and attribute constraints in a single regular expression. In this paper, we investigate an algorithmic aspect of Clark's mechanism (called "attribute-element constraints"), namely, intersection and difference operations, which have been proved to be important in static typechecking for XML processing programs. The contributions here are (1) proofs of closure under intersection and difference and (2) algorithm formulations incorporating a "divide-and-conquer" strategy for avoiding an exponential blow-up for typical inputs.