Acta Informatica

, Volume 51, Issue 5, pp 327–337 | Cite as

Controlled finite automata

  • Alexander Meduna
  • Petr Zemek
Original Article


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.


Turing Machine Transitive Closure Regular Language Finite Automaton Derivation Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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.


  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)Google Scholar
  2. 2.
    Csuhaj-Varjú, E., Masopust, T., Vaszil, G.: Blackhole pushdown automata. Fundam. Inform. 112(2–3), 137–156 (2011)zbMATHGoogle Scholar
  3. 3.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)CrossRefGoogle 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)Google Scholar
  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)Google Scholar
  9. 9.
    Meduna, A.: Automata and Languages: Theory and Applications. Springer, London (2000)CrossRefGoogle Scholar
  10. 10.
    Meduna, A., Masopust, T.: Self-regulating finite automata. Acta Cybern. 18(1), 135–153 (2007)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, Vol. 2: Linear Modeling: Background and Application. Springer, New York (1997)Google Scholar
  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)Google Scholar
  13. 13.
    Wood, D.: Theory of Computation: A Primer. Addison-Wesley, Boston (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Information Systems, Faculty of Information Technology, IT4Innovations Centre of ExcellenceBrno University of TechnologyBrnoCzech Republic

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