Abstract
We enrich the concept of automata with storage by weights taken from any unital valuation monoid. We prove a Chomsky-Schützenberger theorem for the class of weighted languages recognizable by such weighted automata with storage.
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References
Aho, A.V.: Indexed grammars – an extension of context-free grammars. J. ACM 15, 647–671 (1968)
Aho, A.V.: Nested stack automata. JACM 16, 383–406 (1969)
Chomsky, N., Schützenberger, M.P.: The algebraic theory of context-free languages. In: Computer Programming and Formal Systems, pp. 118–161. North-Holland, Amsterdam (1963)
Damm, W.: The IO- and OI-hierarchies. Theoret. Comput. Sci. 20, 95–207 (1982)
Damm, W., Goerdt, A.: An automata-theoretical characterization of the OI-hierarchy. Inform. Control 71, 1–32 (1986)
Denkinger, T.: A Chomsky-Schützenberger representation for weighted multiple context-free languages. In: The 12th International Conference on Finite-State Methods and Natural Language Processing (FSMNLP 2015) (2015). (accepted for publication)
Droste, M., Meinecke, I.: Describing average- and longtime-behavior by weighted MSO logics. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 537–548. Springer, Heidelberg (2010)
Droste, M., Meinecke, I.: Weighted automata and regular expressions over valuation monoids. Intern. J. of Found. of Comp. Science 22(8), 1829–1844 (2011)
Droste, M., Vogler, H.: The Chomsky-Schützenberger theorem for quantitative context-free languages. In: Béal, M.-P., Carton, O. (eds.) DLT 2013. LNCS, vol. 7907, pp. 203–214. Springer, Heidelberg (2013)
Eilenberg, S.: Automata, Languages, and Machines - Volume A. Pure and Applied Mathematics, vol. 59. Academic Press (1974)
Engelfriet, J.: Iterated pushdown automata and complexity classes. In: Proc. of STOCS 1983, pp. 365–373. ACM, New York (1983)
Engelfriet, J.: Context-free grammars with storage. Technical Report 86–11, University of Leiden (1986). see also: arXiv:1408.0683 [cs.FL] (2014)
Engelfriet, J., Schmidt, E.M.: IO and OI.I. J. Comput. System Sci. 15(3), 328–353 (1977)
Engelfriet, J., Vogler, H.: Pushdown machines for the macro tree transducer. Theoret. Comput. Sci. 42(3), 251–368 (1986)
Engelfriet, J., Vogler, H.: High level tree transducers and iterated pushdown tree transducers. Acta Inform. 26, 131–192 (1988)
Fischer, M.J.: Grammars with macro-like productions. Ph.D. thesis, Harvard University, Massachusetts (1968)
Fratani, S., Voundy, E.M.: Dyck-based characterizations of indexed languages. published on arXiv http://arxiv.org/abs/1409.6112 (March 13, 2015)
Ginsburg, S., Greibach, S.A.: Abstract families of languages. Memoirs of the American Math. Soc. 87, 1–32 (1969)
Ginsburg, S., Greibach, S.A.: Principal AFL. J. Comput. Syst. Sci. 4, 308–338 (1970)
Greibach, S.A.: Checking automata and one-way stack languages. J. Comput. System Sci. 3, 196–217 (1969)
Greibach, S.A.: Full AFLs and nested iterated substitution. Inform. Control 16, 7–35 (1970)
Harrison, M.A.: Introduction to Formal Language Theory, 1st edn. Addison-Wesley Longman Publishing Co., Inc, Boston (1978)
Hulden, M.: Parsing CFGs and PCFGs with a Chomsky-Schützenberger representation. In: Vetulani, Z. (ed.) LTC 2009. LNCS, vol. 6562, pp. 151–160. Springer, Heidelberg (2011)
Kambites, M.: Formal languages and groups as memory. arXiv:math/0601061v2 [math.GR] (October 19, 2007)
Kanazawa, M.: Multidimensional trees and a Chomsky-Schützenberger-Weir representation theorem for simple context-free tree grammars. J. Logic Computation (2014)
Maslov, A.N.: The hierarchy of indexed languages of an arbitrary level. Soviet Math. Dokl. 15, 1170–1174 (1974)
Maslov, A.N.: Multilevel stack automata. Probl. Inform. Transm. 12, 38–42 (1976)
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)
Salomaa, A., Soittola, M.: Automata-Theoretic Aspects of Formal Power Series. Texts and Monographs in Computer Science. Springer-Verlag (1978)
Scott, D.: Some definitional suggestions for automata theory. J. Comput. System Sci. 1, 187–212 (1967)
Wand, M.: An algebraic formulation of the Chomsky hierarchy. In: Manes, E.G. (ed.) Category Theory Applied to Computation and Control. LNCS, vol. 25, pp. 209–213. Springer, Heidelberg (1975)
Weir, D.J.: Characterizing Mildly Context-Sensitive Grammar Formalisms. Ph.D. thesis, University of Pennsylvania (1988)
Yoshinaka, R., Kaji, Y., Seki, H.: Chomsky-Schützenberger-type characterization of multiple context-free languages. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 596–607. Springer, Heidelberg (2010)
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Herrmann, L., Vogler, H. (2015). A Chomsky-Schützenberger Theorem for Weighted Automata with Storage. In: Maletti, A. (eds) Algebraic Informatics. CAI 2015. Lecture Notes in Computer Science(), vol 9270. Springer, Cham. https://doi.org/10.1007/978-3-319-23021-4_11
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DOI: https://doi.org/10.1007/978-3-319-23021-4_11
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