Cooperation in Context-Free Grammars

A new dynamical measure of the descriptional complexity for context-free grammars and languages, namely the degree of cooperation, is introduced and studied. This measure is connected with respect to both families of languages considered, namely the regular and context-free languages. We prove that the degree of cooperation is computable for regular and unambigous context-free grammars and it is not computable for arbitrary context-free grammars. The computability status of this measure for languages remains to be investigated.