Descriptional complexity measures of context-free languages

In [2], [3] and [4] several measures of descriptional complexity of context-free grammars (cfg's) and context-free languages (cfl's) have been investigated, most of them having the following properties: 1. The corresponding hierarchy of complexity classes of languages over two-letter alphabets is infinite. 2. The basic algorithmic problems are undecidable. (For example, the problems to determine the complexity of a language generated by a given grammar, to decide whether the given grammar is minimal or to construct an equivalent minimal grammar.) In the present paper an attempt is made to investigate measures which seem to be simpler from two points of view. Over a fixed alphabet they induce a finite hierarchy of languages, and to determine the complexity of a grammar only a part of the grammar has to be considered. In spite of this for most of these new measures the basic algorithmic problems remain to be undecidable.