The Computational Capability of Chemical Reaction Automata

  • Fumiya Okubo
  • Takashi Yokomori
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8727)

Abstract

We propose a new computing model called chemical reaction automata (CRAs) as a simplified variant of reaction automata (RAs) studied in recent literature ([7-9]).

We show that CRAs in maximally parallel manner are computationally equivalent to Turing machines, while the computational power of CRAs in sequential manner coincides with that of the class of Petri nets, which is in marked contrast to the result that RAs (in both maximally parallel and sequential manners) have the computing power of Turing universality ([7-9]). Intuitively, CRAs are defined as RAs without inhibitor functioning in each reaction, providing an offline model of computing by chemical reaction networks (CRNs).

Thus, the main results in this paper not only strengthen the previous result on Turing computability of RAs but also clarify the computing powers of inhibitors in RA computation.

Keywords

Chemical reaction automata Reaction automata Chemical reaction networks Turing computability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.): Multiset Processing. LNCS, vol. 2235. Springer, Heidelberg (2001)MATHGoogle Scholar
  2. 2.
    Csuhaj-Varju, E., Ibarra, O.H., Vaszil, G.: On the computational complexity of P automata. Natural Computing 5, 109–126 (2006)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Csuhaj-Varju, E., Vaszil, G.: P automata. In: The Oxford Handbook of Membrane Computing, pp. 145–167 (2010)Google Scholar
  4. 4.
    Ehrenfeucht, A., Rozenberg, G.: Reaction systems. Fundamenta Informaticae 75, 263–280 (2007)MATHMathSciNetGoogle Scholar
  5. 5.
    Fischer, P.C.: Turing Machines with Restricted Memory Access. Inform. and Contr. 9(4), 364–379 (1966)CrossRefMATHGoogle Scholar
  6. 6.
    Hopcroft, J.E., Motwani, T., Ullman, J.D.: Introduction to automata theory, language and computation, 2nd edn. Addison-Wesley (2003)Google Scholar
  7. 7.
    Okubo, F.: Reaction automata working in sequential manner. RAIRO Theoretical Informatics and Applications 48, 23–38 (2014)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Okubo, F., Kobayashi, S., Yokomori, T.: Reaction automata. Theoretical Computer Science 429, 247–257 (2012)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Okubo, F., Kobayashi, S., Yokomori, T.: On the properties of language classes defined by bounded reaction automata. Theoretical Computer Science 454, 206–221 (2012)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Peterson, J.L.: Petri Net Theory and the Modeling of Systems. Prentice-Hall, Englewood Cliffs (1981)Google Scholar
  11. 11.
    Qian, L., Soloveichik, D., Winfree, E.: Efficient Turing-Universal Computation with DNA Polymers. In: Sakakibara, Y., Mi, Y. (eds.) DNA 16. LNCS, vol. 6518, pp. 123–140. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Natural Computing 7(4), 615–633 (2008)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Suzuki, Y., Fujiwara, Y., Takabayashi, J., Tanaka, H.: Artificial Life Applications of a Class of P Systems: Abstract Rewriting Systems on Multisets. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 299–346. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Thachuk, C., Condon, A.: Space and energy efficient computation with DNA strand displacement systems. In: Stefanovic, D., Turberfield, A. (eds.) DNA 18. LNCS, vol. 7433, pp. 135–149. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Fumiya Okubo
    • 1
  • Takashi Yokomori
    • 2
  1. 1.Faculty of Arts and ScienceKyushu UniversityNishi-ku, FukuokaJapan
  2. 2.Department of Mathematics, Faculty of Education and Integrated Arts and SciencesWaseda UniversityShinjuku-kuJapan

Personalised recommendations