A guide to membrane computing

@article{Paun2002AGT,
  title={A guide to membrane computing},
  author={Gheorghe Paun and Grzegorz Rozenberg},
  journal={Theor. Comput. Sci.},
  year={2002},
  volume={287},
  pages={73-100}
}

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References

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TLDR
It is proved that P systems are able to characterize the one-letter recursively enumerable languages (equivalently, the recursically enumerable sets of natural numbers), providing that an extra feature is considered: the membranes can be made thicker or thinner and the communication through a membrane is possible only when its thickness is equal to 1.
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TLDR
It is proved that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice.
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TLDR
A general class of membrane systems, where besides rules for objects evolution, there are rules for moving objects from a compartment to another one, and for handling membranes, and this latter feature is important, because it makes possible to interpret several DNA computing experiments as membrane computations.
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It is proved that P systems of this type can generate all recursively enumerable sets of numbers and the first time that a polynomial solution to an NP-complete problem has been obtained in the P system framework without making use of the (non-realistic) operation of membrane division.
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This paper considers systems with string-objects processed by rewriting, with the communication controlled by conditions on the contents of the strings, and obtained variants lead to new characterizations of recursively enumerable languages.
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It is proved that a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects, is not only computationally universal, but also able to solve NP complete problems in polynomial time.
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The fundamental properties of computations in such P systems with external output are investigated, including the computing power, normal forms, and basic decision problems.
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