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On regular realizability problems for context-free languages

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Abstract

We consider regular realizability problems, which consist in verifying whether the intersection of a regular language which is the problem input and a fixed language (filter) which is a parameter of the problem is nonempty. We study the algorithmic complexity of regular realizability problems for context-free filters. This characteristic is consistent with the rational dominance relation of CF languages. However, as we prove, it is more rough. We also give examples of both P-complete and NL-complete regular realizability problems for CF filters. Furthermore, we give an example of a subclass of CF languages for filters of which the regular realizability problems can have an intermediate complexity. These are languages with polynomially bounded rational indices.

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References

  1. Rubtsov, A.A., On Prompting Regular Languages in the Model of Generalized Nondeterministic Automata, in Matematicheskie modeli i zadachi upravleniya (Mathematical Models and Control), Moscow: Moscow Inst. of Physics and Technology, 2011, pp. 61–67.

    Google Scholar 

  2. Anderson, T., Loftus, J., Rampersad, N., Santean, N., and Shallit, J., Detecting Palindromes, Patterns and Borders in Regular Languages, Inform. and Comput., 2009, vol. 207, no. 11, pp. 096–1118.

    Article  MathSciNet  Google Scholar 

  3. Vyalyi, M.N., On Regular Realizability, Probl. Peredachi Inf., 2011, vol. 47, no. 4, pp. 43–54 [Probl. Inf. Trans. (Engl. Transl.), 2011, vol. 47, no. 4, pp. 342–352].

    MathSciNet  Google Scholar 

  4. Vyalyi, M.N., On Expressive Power of Regular Realizability, Probl. Peredachi Inf., 2013, vol. 49, no. 3, pp. 86–104 [Probl. Inf. Trans. (Engl. Transl.), 2013, vol. 49, no. 3, pp. 276–291].

    MathSciNet  Google Scholar 

  5. Berstel, J., Transductions and Context-Free Languages, Stuttgart: Teubner, 1979.

    Book  MATH  Google Scholar 

  6. Autebert, J.-M., Beauquier, J., Boasson, L., and Nivat, M., Quelques problémes ouverts en théorie des langages algébriques, RAIRO Inform. Théor., 1979, vol. 13, no. 4, pp. 363–378.

    MATH  MathSciNet  Google Scholar 

  7. Pierre, L. and Farinone, J.-M., Context-Free Languages with Rational Index in ¦¨(n¦Ë) for Algebraic Numbers ¦Ë, RAIRO Inform. Théor. Appl., 1990, vol. 24, no. 3, pp. 275–322.

    MATH  MathSciNet  Google Scholar 

  8. Arora, S. and Barak, B., Computational Complexity: A Modern Approach, Cambridge, UK: Cambridge Univ. Press, 2009.

    Book  Google Scholar 

  9. Sipser, M., Introduction to the Theory of Computation, Boston, MA: Course Technology Cengage Learning, 2012, 3rd ed.

    Google Scholar 

  10. Berstel, J. and Boasson, L., Context-Free Languages, Handbook of Theoretical Computer Science, van Leewen, J., Ed., Amsterdam: Elsevier, 1990, vol. B, pp. 59–102.

    MathSciNet  Google Scholar 

  11. Word, Language, Grammar, vol. 1 of Handbook of Formal Languages, Rozenberg, G. and Salomaa, A., Eds., Berlin: Springer, 1997.

  12. Greibach, S.A., An Infinite Hierarchy of Context-Free Languages, J. ACM, 1969, vol. 16, no. 1, pp. 91–106.

    Article  MATH  MathSciNet  Google Scholar 

  13. Greenlaw, R., Hoover, H.J., and Ruzzo, W.L., Limits to Parallel Computation: P-Completeness Theory, New York: Oxford Univ. Press, 1995.

    MATH  Google Scholar 

  14. Boasson, L., Non-générateurs algébriques et substitution, RAIRO Inform. Théor., 1985, vol. 19, no. 2, pp. 25–136.

    MathSciNet  Google Scholar 

  15. Yakaryιlmaz, A., One-Counter Verifiers for Decidable Languages, Computer Science¡ªTheory and Applications (Proc. 8th Int. Computer Science Sympos. in Russia (CSR’2013), Ekaterinburg, Russia, June 25–29, 2013), Bulatov, A.A. and Shur, A.M., Eds., Lect. Notes Comput. Sci., vol. 7913, Heidelberg: Springer, 2013, pp. 366–377.

    Article  Google Scholar 

  16. Boasson, L., Courcelle, B., and Nivat, M., The Rational Index: A Complexity Measure for Languages, SIAM J. Comput., 1981, vol. 10, no. 2, pp. 284–296.

    Article  MATH  MathSciNet  Google Scholar 

  17. Pierre, L., Rational Indexes of Generators of the Cone of Context-Free Languages, Theoret. Comput. Sci., 1992, vol. 95, no. 2, pp. 279–305.

    Article  MATH  MathSciNet  Google Scholar 

  18. Lewis, P.M., Stearns, R.E., and Hartmanis, J., Memory Bounds for Recognition of Context-Free and Context-Sensitive Languages, in Proc. 6th Annual Sympos. on Switching Circuit Theory and Logical Design (SWCT’1965), Ann Arbor, MI, USA, Oct. 6–8, 1965, New York: IEEE, 1965, pp. 191–202.

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow, Russia

    M. N. Vyalyi

  2. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    M. N. Vyalyi

  3. National Research University—Higher School of Economics, Moscow, Russia

    M. N. Vyalyi & A. A. Rubtsov

  4. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    A. A. Rubtsov

Authors
  1. M. N. Vyalyi
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  2. A. A. Rubtsov
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Correspondence to M. N. Vyalyi.

Additional information

Original Russian Text © M.N. Vyalyi, A.A. Rubtsov, 2015, published in Problemy Peredachi Informatsii, 2015, Vol. 51, No. 4, pp. 47–59.

Supported in part by the Russian Foundation for Basic Research, project no. 12-01-00864, and the President of the Russian Federation Council for State Support of Leading Scientific Schools, project no. NSh-4652.2012.1.

Supported in part by the Russian Foundation for Basic Research, project no. 14-01-00641.

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Vyalyi, M.N., Rubtsov, A.A. On regular realizability problems for context-free languages. Probl Inf Transm 51, 349–360 (2015). https://doi.org/10.1134/S0032946015040043

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