Natural Computing

, Volume 10, Issue 1, pp 167–182 | Cite as

P systems with active membranes: trading time for space

  • Antonio E. Porreca
  • Alberto Leporati
  • Giancarlo Mauri
  • Claudio Zandron


We consider recognizer P systems having three polarizations associated to the membranes, and we show that they are able to solve the PSPACE-complete problem Quantified 3SAT when working in polynomial space and exponential time. The solution is uniform (all the instances of a fixed size are solved by the same P system) and uses only communication rules: evolution rules, as well as membrane division and dissolution rules, are not used. Our result shows that, as it happens with Turing machines, this model of P systems can solve in exponential time and polynomial space problems that cannot be solved in polynomial time, unless P = SPACE.


Membrane computing Computational complexity Register machines 



We would like to thank Damien Woods for the suggestion to avoid object evolution rules in our solution to Q3SAT. This work was partially supported by the Italian project FIAR 2007 “Modelli di calcolo naturale e applicazioni alla Systems Biology”.


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Antonio E. Porreca
    • 1
  • Alberto Leporati
    • 1
  • Giancarlo Mauri
    • 1
  • Claudio Zandron
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanItaly

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