Abstract
We present a systematic investigation of the relationships between various pumping properties—the classic pumping condition of Bar-Hillelet 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.
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Aho, A. V., and Ullman, J. D. (1972),The Theory of Parsing, Translation, and Compiling, Vol. 1, Prentice-Hall, Englewood Cliffs, N.J.
Berstel, J. (1979),Transductions and Context-Free Languages, Teubner, Stuttgart.
Bader, C., and Moura, A. (1982), A generalization of Ogden's lemma,J. Assoc. Comput. Mach.,29(2), 404–407.
Bar-Hillel, Y., Perles, M., and Shamir, E. (1961), On formal properties of simple phrase structure grammars,Z. Phonetik. Sprachwiss. Komm.,14, 143–172.
Boasson, L., and Horváth, S. (1978), On languages satisfying Ogden's lemma,RAIRO Inform. Théor.,12(3), 201–202.
Boonyavatana, R., and Slutzki, G. (1985), Ogden's lemma for nonterminal bounded languages,Theoret. Inform. Appl.,20(4), 457–471.
Boonyavatana, R., and Slutzki, G. (1985), A generalized Ogden's lemma for linear context-free languages,EATCS Bull., No. 28, 20–26.
Grant, P. W. (1982), Extensions of Sokolowski's theorem to prove languages are not context-free or not regular,Internat. J. Comput. Math.,11, 187–196.
Greibach, S. A. (1979), Linearity is polynomially decidable for realtime pushdown store automata,Inform. and Control,12, 27–37.
Harrison, M. A. (1978),Introduction to Formal Language Theory, Addison-Wesley, Reading, MA.
Hopcroft, J. E., and Ullman, J. D. (1979),Introduction to Automata Theory, Languages and Computation, Addison-Wesley, Reading, MA.
Horváth, S. (1978), The family of languages satisfying Bar-Hillel's lemma,RAIRO Inform. Théor.,12(3), 193–199.
Horváth, S. (1983), A comparison of iteration conditions on formal languages,Proc. Colloq. Algebra, Combinatorics and Logic in Computer Science, Györ, Hungary, 12–16 September, 1983 (J. Demetrovics, Gy. Katona, and A. Salomaa, eds.), Colloquia Mathematica Societatis János Bolyai, Vol. 42, J. Bolyai Math. Soc., Budapest, and North-Holland, Amsterdam, 1986, pp. 453–463.
Nijholt, A. (1982), A note on the sufficiency of Sokolowski's criterion for context-free languages,Inform. Process. Lett.,14(5), 207.
Ogden, W. (1968), A helpful result for proving inherent ambiguity,Math. Systems Theory,2(3), 191–194.
Parikh, R. J. (1966), On context-free languages,J. Assoc. Comput. Mach.,13, 570–581.
Sokolowski, S. (1978), A method for proving programming languages non-context-free,Inform. Process. Lett.,7(3), 151–153.
Wise, D. S. (1976), A strong pumping lemma for context-free languages,Theoret. Comput. Sci.,3, 359–369.
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Hewett, R., Slutzki, G. Comparisons between some pumping conditions for context-free languages. Math. Systems Theory 21, 223–233 (1988). https://doi.org/10.1007/BF02088014
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DOI: https://doi.org/10.1007/BF02088014