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Characterizing PSPACE with shallow non-confluent P systems

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Abstract

In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-confluence allows them to solve conjecturally harder problems than confluent P systems, thus reaching \(\mathbf{PSPACE }\). Here we show that \(\mathbf{PSPACE }\) is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-confluence to shallow P systems is equal to the power gained by confluent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth.

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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, Luca Manzoni, Giancarlo Mauri, Antonio E. Porreca & Claudio Zandron

  2. Aix Marseille Université, Université de Toulon, CNRS, LIS, 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. Characterizing PSPACE with shallow non-confluent P systems. J Membr Comput 1, 75–84 (2019). https://doi.org/10.1007/s41965-019-00011-4

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  • DOI: https://doi.org/10.1007/s41965-019-00011-4

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