Controlled finite automata

Abstract

This paper discusses finite automata regulated by control languages over their states and transition rules. It proves that under both regulations, regular-controlled finite automata and context-free-controlled finite automata characterize the family of regular languages and the family of context-free languages, respectively. It also establishes conditions under which any state-controlled finite automaton can be turned into an equivalent transition-controlled finite automaton and vice versa. The paper also demonstrates a close relation between these automata and programmed grammars. Indeed, it proves that finite automata controlled by languages generated by propagating programmed grammars with appearance checking are computationally complete. In fact, it demonstrates that this computational completeness holds even in terms of these automata with a reduced number of states.

This is a preview of subscription content, access via your institution.

Fig. 1

References

  1. 1.

    Csuhaj-Varjú, E., Masopust, T., Vaszil, G.: Blackhole state-controlled regulated pushdown automata. In: Second Workshop on Non-Classical Models for Automata and Applications (NCMA 2010) pp. 45–56 (2010)

  2. 2.

    Csuhaj-Varjú, E., Masopust, T., Vaszil, G.: Blackhole pushdown automata. Fundam. Inform. 112(2–3), 137–156 (2011)

    MATH  Google Scholar 

  3. 3.

    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)

    Google Scholar 

  4. 4.

    Hopcroft, J., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Addison-Wesley, Boston (2000)

    Google Scholar 

  5. 5.

    Jantzen, M., Kudlek, M., Zetzsche, G.: Finite automata controlled by Petri nets. In: Proceedings of the 14th Workshop; Algorithmen und Werkzeuge für Petrinetze. Technical Report Nr. 25/2007, pp. 57–62. Universität Koblenz-Landau (2007)

  6. 6.

    Kolář, D., Meduna, A.: Regulated pushdown automata. Acta Cybern. 2000(4), 653–664 (2000)

    Google Scholar 

  7. 7.

    Kolář, D., Meduna, A.: One-turn regulated pushdown automata and their reduction. Fundam. Inform. 2001(21), 1001–1007 (2001)

    Google Scholar 

  8. 8.

    Kolář, D., Meduna, A.: Regulated automata: from theory towards applications. In: Proceeding of 8th International Conference on Information Systems Implementation and Modelling (ISIM’05) pp. 33–48 (2005)

  9. 9.

    Meduna, A.: Automata and Languages: Theory and Applications. Springer, London (2000)

    Google Scholar 

  10. 10.

    Meduna, A., Masopust, T.: Self-regulating finite automata. Acta Cybern. 18(1), 135–153 (2007)

    MATH  MathSciNet  Google Scholar 

  11. 11.

    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, Vol. 2: Linear Modeling: Background and Application. Springer, New York (1997)

  12. 12.

    Rychnovský, L.: Regulated pushdown automata revisited. In: Proceedings of the 15th Conference STUDENT EEICT 2009, pp. 440–444. Faculty of Information Technology BUT, Brno, CZ (2009)

  13. 13.

    Wood, D.: Theory of Computation: A Primer. Addison-Wesley, Boston (1987)

    Google Scholar 

Download references

Acknowledgments

This work was supported by the following grants: MŠMT CZ1.1.00/02.0070 and TAČR TE01010415. The authors thank the anonymous referee for useful comments regarding the first version of this paper.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Petr Zemek.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Meduna, A., Zemek, P. Controlled finite automata. Acta Informatica 51, 327–337 (2014). https://doi.org/10.1007/s00236-014-0199-5

Download citation

Keywords

  • Turing Machine
  • Transitive Closure
  • Regular Language
  • Finite Automaton
  • Derivation Step