Advertisement

Minimal Reaction Systems Defining Subset Functions

  • Arto SalomaaEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8808)

Abstract

In reaction systems introduced by Ehrenfeucht and Rozenberg the number of resources is essential when various questions concerning generative capacity are investigated. While almost all functions from the set of subsets of a finite set \(S\) into itself can be defined by unrestricted reaction systems, only a specific subclass of such functions is defined by minimal reaction systems. In this paper we show that also minimal reaction systems suffice for defining all such functions, provided repetitive use is allowed. Specifically, everything generated by an arbitrary reaction system is generated by a minimal one in three steps. In this way also some functions not at all definable by reaction systems can be generated by minimal reaction systems. All subsets of \(S\), in any prechosen order, appear in the sequence of a minimal reaction system.

Keywords

Reaction system Reactant Inhibitor Universality of minimal resources Subset function Sequence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brijder, R., Ehrenfeucht, A., Main, M., Rozenberg, G.: A tour of reaction systems. International Journal of Foundations of Computer Science 22, 1499–1517 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ehrenfeucht, A., Kleijn, J., Koutny, M., Rozenberg, G.: Minimal reaction systems. In: Priami, C., Petre, I., de Vink, E. (eds.) Transactions on Computational Systems Biology XIV. LNCS, vol. 7625, pp. 102–122. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Ehrenfeucht, A., Main, M., Rozenberg, G.: Functions defined by reaction systems. International Journal of Foundations of Computer Science 22, 167–178 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ehrenfeucht, A., Rozenberg, G.: Reaction systems. Fundamenta Informaticae 7, 263–280 (2007)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Ehrenfeucht, A., Rozenberg, G.: Zoom structures and reaction systems yield exploration systems. International Journal of Foundations of Computer Science (to appear, 2014)Google Scholar
  6. 6.
    Formenti, E., Manzoni, L., Porreca, A.E.: On the complexity of occurrence and convergence problems for reaction systems. Natural Computing (to appear, 2014)Google Scholar
  7. 7.
    Montagna, F., Rozenberg, G.: On minimal reaction systems, forthcoming. (G. Rozenberg, personal communication.)Google Scholar
  8. 8.
    Piccard, S.: Sur les bases du groupe symétrique et les couples de substitutions qui engendrent un goupe régulier. Librairie Vuibert, Paris (1946)zbMATHGoogle Scholar
  9. 9.
    Salomaa, A.: Composition sequences for functions over a finite domain. Theoretical Computer Science 292, 263–281 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Salomaa, A.: On state sequences defined by reaction systems. In: Constable, R.L., Silva, A. (eds.) Logic and Program Semantics, Kozen Festschrift. LNCS, vol. 7230, pp. 271–282. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Salomaa, A.: Functions and sequences generated by reaction systems. Theoretical Computer Science 466, 87–96 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Salomaa, A.: Functional constructions between reaction systems and propositional logic. International Journal of Foundations of Computer Science 24, 147–159 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Salomaa, A.: Minimal and almost minimal reaction systems. Natural Computing 12, 369–376 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Salomaa, A.: Compositions of reaction systems. Submitted for publication (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Turku Centre for Computer ScienceTurkuFinland

Personalised recommendations