Abstract
We solve affirmatively a new special case of the P conjecture by Gh. Păun, which states that P systems with active membranes without charges and without non-elementary membrane division cannot solve \(\mathbf {NP}\)-complete problems in polynomial time. The variant we consider is monodirectional, i.e., without send-in communication rules, shallow, i.e., with membrane structures consisting of only one level besides the external membrane, and deterministic, rather than more generally confluent. We describe a polynomial-time Turing machine simulation of this variant of P systems, exploiting a generalised version of dependency graphs for P systems which, unlike the original version introduced by Cordón-Franco et al., also takes membrane dissolution into account.
This work was partially supported by Fondo d’Ateneo 2016 of Università degli Studi di Milano-Bicocca, project 2016-ATE-0492 “Sistemi a membrane: classi di complessità spaziale e temporale”.
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Notes
- 1.
The determinism of the P systems is not explicitly stated in the original paper [8], but can be easily checked by inspection of the rules.
- 2.
- 3.
That is, node \((\mathsf {yes},\mathrm {env})\) in the original notation.
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Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C. (2018). Solving a Special Case of the P Conjecture Using Dependency Graphs with Dissolution. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. CMC 2017. Lecture Notes in Computer Science(), vol 10725. Springer, Cham. https://doi.org/10.1007/978-3-319-73359-3_13
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