XML schemas without order

XML schemas consist of context-free grammars that allow regular expressions on the right-hand side of productions. In the schema definition language ScmDL, XML schemas are enhanced to, among other things, mark nodes as ordered or as unordered. An unordered node is then derived by a production with a regular expression r if the string induced by its children belongs to the symmetric closure of r. The symmetric closure of r consists of all permutations of all strings in r. We say that a language is unordered if it equals its symmetric closure. In this paper we also consider various other formalisms to specify unordered languages: shuffle expressions, order-invariant regular expressions, and two logical languages Lmod,� and L�. The latter allow to express modular and/orconstraints on the number of times symbols can occur. We characterize the expressiveness of the mentioned formalisms and consider the complexity of their equivalence problem. We conclude that nearly all these formalisms are too expressive: they allow to specify complex languages with little practical significance. Therefore, we propose to use the logics Lor L�� to express unordered languages.