In this paper we compare Parikh´s condition to, firstly, various pumping conditions (the pumping lemma of Bar-Hillel. Ogden´s condition and Bader-Moura condition); and secondly, to interchange and linear interchange conditions. In order to carry out these comparisons we show some interesting properties of semilinear languages. The central results of this paper is the orthogonality of previous related pumping and interchange conditions and Pariskh´s one.
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