properly includes the TAG-equivalent formalisms but is properly included in the unrestricted LCFRS/MCFG hierarchy. Characterization Despite a considerable amount of work on the subject, there is no generally accepted formal definition of mild context-sensitivity. According to the original characterization by Joshi, a class of mildly context-sensitive grammars should have the following properties: limited cross-serial dependencies constant growth polynomial parsing In addition to these, it is understood that every class of mildly context-sensitive grammars should be able to generate all context-free languages. Joshi’s characterization is not a formal definition. He notes: Other authors have proposed alternative characterizations of mild context-sensitivity, some of which take the form of formal definitions. For example, Laura Kallmeyer takes the perspective that mild context-sensitivity should be defined as a property of classes of languages rather than, as in Joshi’s characterization, classes of grammars. Such a language-based definition leads to a different notion of the concept than Joshi’s. Cross-serial dependencies The term cross-serial dependencies refers to certain characteristic word ordering patterns, in particular to the verb–argument patterns observed in subordinate clauses in Dutch and Swiss German. These are the very patterns that can be used to argue against the context-freeness of natural language; thus requiring mildly context-sensitive grammars to model cross-serial dependencies means that these grammars must be more powerful than context-free grammars. Kallmeyer identifies the ability to model cross-serial dependencies with the ability to generate the copy language and its generalizations to two or more copies of w, up to some bound. These languages are not context-free, which can be shown using the pumping lemma. Constant growth A formal language is of constant growth if every string in the language is longer than the next shorter strings by at most a (language-specific) constant. Languages that violate this property are often considered to be beyond human capacity, although some authors have argued that certain phenomena in natural language do show a growth that cannot be bounded by a constant. Most mildly context-sensitive grammar formalisms (in particular, LCFRS/MCFG) actually satisfy a stronger property than constant growth called semilinearity. A language is semilinear if its image under the Parikh-mapping (the mapping that "forgets" the relative position of the symbols in a string, effectively treating it as a bag of words) is a regular language. All semilinear languages are of constant growth, but not every language with constant growth is semilinear. Polynomial parsing A grammar formalism is said to have