On the Computational Capacity of Parallel Communicating Finite Automata

  • Henning Bordihn
  • Martin Kutrib
  • Andreas Malcher
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)


Systems of parallel finite automata communicating by states are investigated. We consider deterministic and nondeterministic devices and distinguish four working modes. It is known that systems in the most general mode are as powerful as one-way multihead finite automata. Here we solve some open problems on the computational capacity of systems working in the remaining modes. In particular, it is shown that deterministic returning and non-returning devices are equivalent, and that there are languages which are accepted by deterministic returning and centralized systems but cannot be accepted by deterministic non-returning centralized systems. Furthermore, we show that nondeterministic centralized systems are strictly more powerful than their deterministic variants. Finally, incomparability with the class of (deterministic) (linear) context-free languages as well as the Church-Rosser languages is derived.


Transition Function Finite Automaton Computational Capacity Input Symbol Query State 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brand, D., Zafiropulo, P.: On communicating finite-state machines. J. ACM 30, 323–342 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Buda, A.: Multiprocessor automata. Inform. Process. Lett. 25, 257–261 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Choudhary, A., Krithivasan, K., Mitrana, V.: Returning and non-returning parallel communicating finite automata are equivalent. RAIRO Inform. Théor. 41, 137–145 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Csuhaj-Varjú, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems: A Grammatical Approach to Distribution and Cooperation. Gordon and Breach, Yverdon (1994)Google Scholar
  5. 5.
    Ďuriš, P., Jurdziński, T., Kutyłowski, M., Loryś, K.: Power of cooperation and multihead finite systems. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 896–907. Springer, Heidelberg (1998)Google Scholar
  6. 6.
    Harrison, M.A., Ibarra, O.H.: Multi-tape and multi-head pushdown automata. Inform. Control 13, 433–470 (1968)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Ibarra, O.H.: On two-way multihead automata. J. Comput. System Sci. 7, 28–36 (1973)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Ibarra, O.H.: A note on semilinear sets and bounded-reversal multihead pushdown automata. Inform. Process. Lett. 3, 25–28 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Jurdziński, T.: The Boolean closure of growing context-sensitive languages. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 248–259. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Klemm, R.: Systems of communicating finite state machines as a distributed alternative to finite state machines. Phd thesis, Pennsylvania State University (1996)Google Scholar
  11. 11.
    Martín-Vide, C., Mateescu, A., Mitrana, V.: Parallel finite automata systems communicating by states. Int. J. Found. Comput. Sci. 13, 733–749 (2002)zbMATHCrossRefGoogle Scholar
  12. 12.
    McNaughton, R., Narendran, P., Otto, F.: Church-Rosser Thue systems and formal languages. J. ACM 35, 324–344 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Rosenberg, A.L.: On multi-head finite automata. IBM J. Res. Dev. 10, 388–394 (1966)zbMATHCrossRefGoogle Scholar
  14. 14.
    Wagner, K., Wechsung, G.: Computational Complexity. Reidel, Dordrecht (1986)Google Scholar
  15. 15.
    Yao, A.C., Rivest, R.L.: k + 1 heads are better than k. J. ACM 25, 337–340 (1978)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Henning Bordihn
    • 1
  • Martin Kutrib
    • 2
  • Andreas Malcher
    • 2
  1. 1.Institut für InformatikUniversität PotsdamPotsdamGermany
  2. 2.Institut für InformatikUniversität GiessenGiessenGermany

Personalised recommendations