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Monodirectional P systems

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Abstract

We investigate the influence that the flow of information in membrane systems has on their computational complexity. In particular, we analyse the behaviour of P systems with active membranes where communication only happens from a membrane towards its parent, and never in the opposite direction. We prove that these “monodirectional P systems” are, when working in polynomial time and under standard complexity-theoretic assumptions, much less powerful than unrestricted ones: indeed, they characterise classes of problems defined by polynomial-time Turing machines with \({\mathbf{NP}}\) oracles, rather than the whole class \({\mathbf{PSPACE}}\) of problems solvable in polynomial space.

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Notes

  1. We define a subconfiguration of \({\mathcal {C}}_i\) as a subtree (a root node together with all its descendents) of the membrane structure of \({\mathcal {C}}_i\), including labels, multisets, and charges of the membranes.

  2. We define a subforest \(F'\) of a forest F to be any subgraph such that, whenever \(F'\) includes a vertex v, it also includes all the descendents of v.

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Acknowledgments

This work was partially supported by Università degli Studi di Milano-Bicocca, FA 2014: “Complessità computazionale nei sistemi a membrane”.

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Correspondence to Alberto Leporati.

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Leporati, A., Manzoni, L., Mauri, G. et al. Monodirectional P systems. Nat Comput 15, 551–564 (2016). https://doi.org/10.1007/s11047-016-9565-2

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