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Simulating Elementary Active Membranes

with an Application to the P Conjecture
  • Alberto Leporati
  • Luca Manzoni
  • Giancarlo Mauri
  • Antonio E. Porreca
  • Claudio Zandron
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8961)

Abstract

The decision problems solved in polynomial time by P systems with elementary active membranes are known to include the class \(\mathbf{P}^{\# \mathbf{P}}\). This consists of all the problems solved by polynomial-time deterministic Turing machines with polynomial-time counting oracles. In this paper we prove the reverse inclusion by simulating P systems with this kind of machines: this proves that the two complexity classes coincide, finally solving an open problem by Păun on the power of elementary division. The equivalence holds for both uniform and semi-uniform families of P systems, with or without membrane dissolution rules. Furthermore, the inclusion in \(\mathbf{P}^{\# \mathbf{P}}\) also holds for the P systems involved in the P conjecture (with elementary division and dissolution but no charges), which improves the previously known upper bound \(\mathbf{PSPACE}\).

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

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

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