All semilinear languages are of constant growth, but not every language with constant growth is semilinear. A grammar formalism is said to have "polynomial parsing" if its membership problem can be solved in deterministic polynomial time. This is the problem to decide, given a grammar "G" written in the formalism and a string "w", whether "w" is generated by "G" – that is, whether "w" is "grammatical" according to "G". The time complexity of this problem is measured in terms of the combined size of "G" and "w". Under the view on mild context-sensitivity as a property of classes of languages, "polynomial parsing" refers to the language membership problem. This is the problem to decide, for a fixed language "L", whether a given string "w" belongs to "L". The time complexity of this problem is measured in terms of the length of "w"; it ignores the question how "L" is specified. Note that both understandings of "polynomial parsing" are idealizations in the sense that for practical applications one is interested not only in the yes/no question whether a sentence is grammatical, but also in the syntactic structure that the grammar assigns to the sentence. Over the years, a large number of grammar formalisms have been introduced that satisfy some or all of the characteristic properties put forth by Joshi. Several of them have alternative, automaton-based characterizations that are not discussed in this article; for example, the languages generated by tree-adjoining grammar can be characterized by embedded pushdown automata. Linear context-free rewriting systems/multiple context-free grammars form a two-dimensional hierarchy of generative power with respect to two grammar-specific parameters called "fan-out" and "rank". More precisely, the languages generated by LCFRS/MCFG with fan-out  and rank  are properly included in the class of languages generated by LCFRS/MCFG with rank  and fan-out "f", as well as the class of languages generated by LCFRS/MCFG with rank "r" and fan-out . In the presence of well-nestedness, this hierarchy collapses to a one-dimensional hierarchy with respect to fan-out; this is because every well-nested LCFRS/MCFG can be transformed into an equivalent well-nested LCFRS/MCFG with the same fan-out and rank 2.