P Systems with Elementary Active Membranes: Beyond NP and coNP

  • Antonio E. Porreca
  • Alberto Leporati
  • Giancarlo Mauri
  • Claudio Zandron
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6501)


We prove that a uniform family of P systems with active membranes, where division rules only operate on elementary membranes and dissolution rules are avoided, can be used to solve the following PP-complete decision problem in polynomial time: given a Boolean formula of m variables in 3CNF, do at least \(\sqrt{2^m}\) among the 2 m possible truth assignments satisfy it? As a consequence, the inclusion \(\mathbf{PP} \subseteq \mathbf{PMC}_{\mathcal{AM}(\mathrm{-d,-n})}\) holds: this provides an improved lower bound on the class of languages decidable by this kind of P systems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 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-BicoccaMilanoItaly

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