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
Article

Abstract

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.

Keywords

Reaction systems Computational complexity Discrete dynamical systems 

References

  1. Ehrenfeucht A, Rozenberg G (2007) Reaction systems. Fundamenta Informaticae 75:263–280. http://iospress.metapress.com/content/b86t11hryvwq69l0/
  2. Ehrenfeucht A, Rozenberg G (2009) Introducing time in reaction systems. Theor Comput Sci 410(4):310–322. doi:10.1016/j.tcs.2008.09.043
  3. Manzoni L, Porreca AE (2013) Reaction systems made simple: a normal form and a classification theorem. In: Mauri G, Dennunzio A, Manzoni L, Porreca AE (eds) Unconventional computation and natural computation, 12th international conference, UCNC 2013, Lecture Notes in Computer Science, vol 7956, Springer, New York, pp 150–161. doi:10.1007/978-3-642-39074-6_15
  4. Manzoni L, Poças D, Porreca AE (2014) Simple reaction systems and their classification. Int J Found Comput Sci 18(6):1197Google Scholar
  5. Papadimitriou CH (1993) Computational complexity. Addison-Wesley, ReadingGoogle Scholar
  6. Salomaa A (2013a) Functional constructions between reaction systems and propositional logic. Int J Found Comput Sci 24(1):147–159. doi:10.1142/S0129054113500044
  7. Salomaa A (2013b) Minimal and almost minimal reaction systems. Nat Comput 12(3):369–376. doi:10.1007/s11047-013-9372-y.
  8. Sutner K (1995) On the computational complexity of finite cellular automata. J Comput Syst Sci 50(1):87–97. doi:10.1006/jcss.1995.1009

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

Personalised recommendations