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Simulating counting oracles with cooperation

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Abstract

Many variants of P systems with active membranes are able to solve traditionally intractable problems. Sometimes they also characterize well known complexity classes, depending upon the computational features they use. In this paper we continue the investigation of the importance of (minimal) cooperative rules to increase the computational power of P systems. In particular, we prove that monodirectional shallow chargeless P systems with active membranes and minimal cooperation working in polynomial time precisely characterise \(\mathbf{P }^{\#{\mathbf{P }}}_{\parallel }\), the complexity class of problems solved in polynomial time by deterministic Turing machines with a polynomial number of parallel queries to an oracle for a counting problem.

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Acknowledgements

Antonio E. Porreca was funded by his salary of French public servant, affiliated to Aix Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France.

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Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336, 20126, Milan, Italy

    Alberto Leporati, Giancarlo Mauri & Claudio Zandron

  2. Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Via Alfonso Valerio 12/a, 24127, Trieste, Italy

    Luca Manzoni

  3. Université Publique, Marseille, France

    Antonio E. Porreca

Authors
  1. Alberto Leporati
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  2. Luca Manzoni
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  3. Giancarlo Mauri
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  4. Antonio E. Porreca
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  5. Claudio Zandron
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Correspondence to Alberto Leporati.

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Leporati, A., Manzoni, L., Mauri, G. et al. Simulating counting oracles with cooperation. J Membr Comput 2, 303–310 (2020). https://doi.org/10.1007/s41965-020-00052-0

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