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Generalized Register Context-Free Grammars

  • Ryoma SendaEmail author
  • Yoshiaki Takata
  • Hiroyuki Seki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11417)

Abstract

Register context-free grammars (RCFG) is an extension of context-free grammars to handle data values in a restricted way. This paper first introduces register type as a finite representation of the register contents and shows some properties of RCFG. Next, generalized RCFG (GRCFG) is defined by permitting an arbitrary relation on data values in the guard expression of a production rule. We extend register type to GRCFG and introduce two properties of GRCFG, the simulation property and the type oracle. We then show that \(\varepsilon \)-rule removal is possible and the emptiness and membership problems are EXPTIME solvable for GRCFG that satisfy these two properties.

References

  1. 1.
    Benedikt, M., Ley, C., Puppis, G.: What you must remember when processing data words. In: 4th Alberto Mendelzon International Workshop on Foundations of Data Management (2010)Google Scholar
  2. 2.
    Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data trees and XML reasoning. J. ACM 56(3), 13:1–13:48 (2009).  https://doi.org/10.1145/1516512.1516515MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bojańczyk, M., David, C., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data words. ACM Trans. Comput. Log. 12(4), 27:1–27:26 (2011).  https://doi.org/10.1145/1970398.1970403MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bojańczyk, M., Klin, B., Lasota, S.: Automata theory in nominal sets. Log. Methods Comput. Sci. 10(3) (2014).  https://doi.org/10.2168/LMCS-10(3:4)2014
  5. 5.
    Bouyer, P.: A logical characterization of data languages. Inf. Process. Lett. 84(2), 75–85 (2002).  https://doi.org/10.1016/S0020-0190(02)00229-6MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cheng, E.Y., Kaminski, M.: Context-free languages over infinite alphabets. Acta Inf. 35(3), 245–267 (1998).  https://doi.org/10.1007/s002360050120MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Demri, S., Lazić, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log. 10(3), 16:1–16:30 (2009).  https://doi.org/10.1145/1507244.1507246MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Demri, S., Lazić, R., Nowak, D.: On the freeze quantifier in constraint LTL: decidability and complexity. Inf. Comput. 205(1), 2–24 (2007).  https://doi.org/10.1016/j.ic.2006.08.003MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Figueira, D., Hofman, P., Lasota, S.: Relating timed and register automata. Math. Struct. Comput. Sci. 26(6), 993–1021 (2016).  https://doi.org/10.1017/S0960129514000322MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kaminski, M., Francez, N.: Finite-memory automata. Theor. Comput. Sci. 134(2), 329–363 (1994).  https://doi.org/10.1016/0304-3975(94)90242-9MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Libkin, L., Martens, W., Vrgoč, D.: Querying graphs with data. J. ACM 63(2), 14:1–14:53 (2016).  https://doi.org/10.1145/2850413MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Libkin, L., Tan, T., Vrgoč, D.: Regular expressions for data words. J. Comput. Syst. Sci. 81(7), 1278–1297 (2015).  https://doi.org/10.1016/j.jcss.2015.03.005MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Libkin, L., Vrgoč, D.: Regular path queries on graphs with data. In: 15th International Conference on Database Theory (ICDT 2012), pp. 74–85 (2012).  https://doi.org/10.1145/2274576.2274585
  14. 14.
    Milo, T., Suciu, D., Vianu, V.: Typechecking for XML transformers. In: 19th ACM Symposium on Principles of Database Systems (PODS 2000), pp. 11–22 (2000).  https://doi.org/10.1145/335168.335171
  15. 15.
    Neven, F., Schwentick, T., Vianu, V.: Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log. 5(3), 403–435 (2004).  https://doi.org/10.1145/1013560.1013562MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Sakamoto, H., Ikeda, D.: Intractability of decision problems for finite-memory automata. Theor. Comput. Sci. 231(2), 297–308 (2000).  https://doi.org/10.1016/S0304-3975(99)00105-XMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Senda, R., Takata, Y., Seki, H.: Complexity results on register context-free grammars and register tree automata. In: Fischer, B., Uustalu, T. (eds.) ICTAC 2018. LNCS, vol. 11187, pp. 415–434. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-02508-3_22CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graduate School of Information ScienceNagoya UniversityChikusa, NagoyaJapan
  2. 2.Graduate School of EngineeringKochi University of TechnologyKami City, KochiJapan

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