Production complexity of some operations on context-free languages

Abstract

We investigate context-free languages with respect to the measure Prod of descriptional complexity, which gives the minimal number of productions necessary to generate the language. In particular, we consider the behaviour of this measure with respect to operations. For given natural numbers c 1,c 2,...,c n and an n-ary operation τ on languages, we discuss the set g τ (c 1,c 2,...,c n ) which is the range of Prod(τ(L 1,L 2,..., L n )) where, for 1 ≥ i ≥ n, L i is a context-free language with Prod(L i ) = c i . The operations under discussion are union, concatenation, reversal, and Kleene closure. © 2012 Springer-Verlag Berlin Heidelberg.