Abstract
We study a family of context-free languages that reduce to \(\varepsilon \) in the free group and give several homomorphic characterizations of indexed languages relevant to that family.
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References
Aho, A.: Indexed grammars-an extension of context-free grammars. J. ACM 15, 647–671 (1968)
Berstel, J.: Transductions and Context-Free Languages. Teubner Verlag, Wiesbaden (1979)
Berstel, J., Boasson, L.: Context-free languages. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science (Vol. B), pp. 59–102. MIT Press, Cambridge (1990)
Berstel, J., Boasson, L.: Balanced grammars and their languages. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, pp. 3–25. Springer, Heidelberg (2002)
Caucal, D.: On infinite transition graphs having a decidable monadic theory. Theor. Comput. Sci. 290(1), 79–115 (2003)
Chomsky, N., Schützenberger, M.P.: The algebraic theory of context-free languages. In: Braffort, P., Hirschberg, D. (eds.) Computer Programming and Formal Systems. Studies in Logic and the Foundations of Mathematics, vol. 35, pp. 118–161. Elsevier, North-Holland (1963). doi:10.1016/S0049-237X(08)72023-8. http://www.sciencedirect.com/science/article/pii/S0049237X08720238. ISSN: 0049-237X
Fischer, M.J.: Grammars with macro-like productions. In: 9th Annual Symposium on Switching and Automata Theory. pp. 131–142. IEEE Computer Society (1968)
Fratani, S.: Automates à piles de piles.. de piles. Ph.D. thesis, Université Bordeaux 1 (2005)
Hague, M., Murawski, A.S., Ong, C.L., Serre, O.: Collapsible pushdown automata and recursion schemes. In: Proceedings LICS, pp. 452–461. IEEE Computer Society (2008)
Hirose, S., Nasu, M.: Left universal context-free grammars and homomorphic characterizations of languages. Inf. Control 50(2), 110–118 (1981)
Kanazawa, M.: Multidimensional trees and a Chomsky-Schützenberger Weir representation theorem for simple context-free tree grammars. J. Logic Comput. (2014). doi:10.1093/logcom/exu043. http://logcom.oxfordjournals.org/content/early/2014/06/30/logcom.exu043.abstract
Knapik, T., Niwiński, D., Urzyczyn, P.: Higher-order pushdown trees are easy. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 205–222. Springer, Heidelberg (2002)
Maslov, A.N.: Hierarchy of indexed languages of arbitrary level. Sov. Math. Dokl 115(14), 1170–1174 (1974)
Maslov, A.N.: Multilevel stack automata. Prob. Inf. Transm. 12, 38–43 (1976)
Mehlhorn, K.: Pebbling mountain ranges and its application to DCFL-recognition. Automata, Lang. Program. 85, 422–435 (1980)
Nivat, M.: Transductions des langages de Chomsky. Ann. Inst. Fourier 18(1), 339–455 (1968)
Okhotin, A.: Non-erasing variants of the Chomsky–Schützenberger theorem. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 121–129. Springer, Heidelberg (2012)
Ong, L.: Higher-order model checking: an overview. In: LICS, pp. 1–15. IEEE Computer Society (2015)
Sorokin, A.: Monoid automata for displacement context-free languages. CoRR abs/1403.6060 (2014)
Weir, D.: Characterizing Mildly Context-Sensitive Grammar Formalisms. Ph.D. thesis, University of Pennsylvania , available as Technical Report MS-CIS-88-74 (1988)
Acknowledgement
The authors would like to thank Pr. Jean-Marc Talbot whose remarks and suggestions greatly improved the development of this paper.
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Fratani, S., Voundy, E.M. (2016). Homomorphic Characterizations of Indexed Languages. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_28
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DOI: https://doi.org/10.1007/978-3-319-30000-9_28
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