Natural Computing

, Volume 14, Issue 1, pp 185–191 | Cite as

On the complexity of occurrence and convergence problems in reaction systems

  • Enrico Formenti
  • Luca Manzoni
  • Antonio E. Porreca


Reaction systems are a model of computation inspired by biochemical reactions introduced by Ehrenfeucht and Rozenberg. Two problems related to the dynamics (the evolution of the state with respect to time) of reaction systems, namely, the occurrence and the convergence problems, were recently investigated by Salomaa. In this paper, we prove that both problems are PSPACE-complete when the numerical parameter of the problems (i.e. the time step when a specified element must appear) is given as input. Moreover, they remain PSPACE-complete even for minimal reaction systems.


Reaction systems Computational complexity Discrete dynamical systems 



This work has been partially supported by the French National Research Agency project EMC (ANR-09-BLAN-0164).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Enrico Formenti
    • 1
  • Luca Manzoni
    • 1
  • Antonio E. Porreca
    • 2
  1. 1.University of Nice Sophia Antipolis, CNRS, I3S, UMR 7271Sophia AntipolisFrance
  2. 2.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanItaly

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