Extremal Combinatorics of Reaction Systems

  • Alberto Dennunzio
  • Enrico Formenti
  • Luca Manzoni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)


Extremal combinatorics is the study of the size that a certain collection of objects must have in order to certainly satisfy a property. Reaction systems are a recent formalism for computation inspired by chemical reactions. This work is a first contribution to the study of the behaviour of large reaction systems by means of extremal combinatorics. We defined several different properties that capture some basic behaviour of a reaction system and we prove that they must necessarily be satisfied by large enough systems. Explicit bounds and formulae are also provided.


Reaction systems extremal combinatorics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ehrenfeucht, A., Main, M., Rozenberg, G.: Combinatorics of life and death for reaction systems. International Journal of Foundations of Computer Science 21, 345–356 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Ehrenfeucht, A., Rozenberg, G.: Basic notions of reaction systems. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 27–29. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Ehrenfeucht, A., Rozenberg, G.: Reaction systems. Fundamenta Informaticae 75, 263–280 (2007)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Graham, R.L., Rothschild, B.L., Spencer, J.H.: Ramsey Theory. Wiley-Interscience Series in Discrete Mathematics and Optimization Advisory. Wiley-Interscience (1990)Google Scholar
  5. 5.
    Jukna, S.: Extremal combinatorics: with applications in computer science. Springer (2001)Google Scholar
  6. 6.
    Salomaa, A.: Functional constructions between reaction systems and propositional logic. International Journal of Foundations of Computer Science 24(1), 147–159 (2013)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alberto Dennunzio
    • 1
  • Enrico Formenti
    • 2
  • Luca Manzoni
    • 2
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano - BicoccaMilanoItaly
  2. 2.Laboratoire I3SUniversité Nice Sophia AntipolisSophia Antipolis CEDEXFrance

Personalised recommendations