Advertisement

Two-Head Finite-State Acceptors with Translucent Letters

  • Benedek Nagy
  • Friedrich Otto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

Finite-state acceptors are studied that have two heads that read the input from opposite sides. In addition, a set of translucent letters is associated with each state. It is shown that these two-head automata are strictly more expressive than the model with a single head, but that they still only accept languages that have a semi-linear Parikh image. In fact, we obtain a characterization for the class of linear context-free trace languages in terms of a specific class of two-head finite-state acceptors with translucent letters.

Keywords

Two-head finite-state acceptor Translucent letter Linear context-free language Semi-linear Parikh set Trace language 

References

  1. 1.
    Bedregal, B.R.C.: Some subclasses of linear languages based on nondeterministic linear automata. arXiv:10276v1 (2016)
  2. 2.
    Diekert, V., Rozenberg, G.: The Book of Traces. World Scientific, Singapore (1995)CrossRefGoogle Scholar
  3. 3.
    Freund, R., Păun, Gh., Rozenberg, G., Salomaa, A.: Watson-Crick finite automata. In: Rubin, H., Wood, D.H. (eds.) DNA Based Computers, Proceedings of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 297–328. DIMACS/AMS (1999)Google Scholar
  4. 4.
    Greibach, S.: A note on undecidable properties of formal languages. Math. Syst. Theory 2, 1–6 (1968)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)zbMATHGoogle Scholar
  6. 6.
    Meduna, A., Zemek, P.: Jumping finite automata. Int. J. Found. Comput. Sci. 23, 1555–1578 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Nagy, B.: On \(5^{\prime } \rightarrow 3^{\prime }\) sensing Watson-Crick finite automata. In: Garzon, M.H., Yan, H. (eds.) DNA 2007. LNCS, vol. 4848, pp. 256–262. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-77962-9_27CrossRefGoogle Scholar
  8. 8.
    Nagy, B.: A class of 2-head finite automata for linear languages. Triangle: Lang. Math. Approaches 8, 89–99 (2012)Google Scholar
  9. 9.
    Nagy, B.: On a hierarchy of \(5^{\prime } \rightarrow 3^{\prime }\)sensing Watson-Crick finite automata languages. J. Log. Comput. 23, 855–872 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Nagy, B., Kovács, L.: Finite automata with translucent letters applied in natural and formal language theory. In: Nguyen, N.T., Kowalczyk, R., Fred, A., Joaquim, F. (eds.) Transactions on Computational Collective Intelligence XVII. LNCS, vol. 8790, pp. 107–127. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44994-3_6CrossRefGoogle Scholar
  11. 11.
    Nagy, B., Otto, F.: CD-systems of stateless deterministic R(1)-automata accept all rational trace languages. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 463–474. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13089-2_39CrossRefzbMATHGoogle Scholar
  12. 12.
    Nagy, B., Otto, F.: An automata-theoretical characterization of context-free trace languages. In: Černá, I., et al. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 406–417. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-18381-2_34CrossRefGoogle Scholar
  13. 13.
    Nagy, B., Otto, F.: CD-systems of stateless deterministic R(1)-automata governed by an external pushdown store. RAIRO Theor. Inform. Appl. 45, 413–448 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Nagy, B., Otto, F.: Finite-state acceptors with translucent letters. In: Bel-Enguix, G., Dahl, V., De La Puente, A.O. (eds.) BILC 2011: AI Methods for Interdisciplinary Research in Language and Biology, Proceedings, pp. 3–13. SciTePress, Portugal (2011)Google Scholar
  15. 15.
    Nagy, B., Otto, F.: On CD-systems of stateless deterministic R-automata with window size one. J. Comput. Syst. Sci. 78, 780–806 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Nagy, B., Otto, F.: Globally deterministic CD-systems of stateless R-automata with window size 1. Int. J. Comput. Math. 90, 1254–1277 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Rosenberg, A.L.: On multi-head finite automata. IBM J. Res. Dev. 10, 388–394 (1966)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Rosenberg, A.L.: A machine realization of the linear context-free languages. Inf. Control 10, 175–188 (1967)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Arts and SciencesEastern Mediterranean UniversityFamagustaTurkey
  2. 2.Fachbereich Elektrotechnik/InformatikUniversität KasselKasselGermany

Personalised recommendations