Comparisons between some pumping conditions for context-free languages

We present a systematic investigation of the relationships between various pumping properties-the classic pumping condition of Bar-Hillel et al., Ogden's condition, a generalized Ogden condition of Bader and Moura, Sokolowski's condition, an extended Sokolowski condition of Grant, and linear versions of some of these conditions. We define special language operations that allow us to produce, in a systematical and uniform way, languages that satisfy some combinations of the pumping conditions but not the others. We show, among others, that the general and the linear pumping conditions are "orthogonal," whereas the generalized Ogden condition is stronger than the extended Sokolowski condition.