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13th International Conference on Membrane Computing - MTA Sztaki

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<strong>Membrane</strong> systems and hypercomputati<strong>on</strong><br />

can also be ‘chained together’ to solve more complex problems. In joint work with<br />

Marian Gheorghe, we have c<strong>on</strong>sidered this problem in detail: we have shown how<br />

a natural extensi<strong>on</strong> of the accelerated P system c<strong>on</strong>cept easily allows us to traverse<br />

all levels of the arithmetic hierarchy, and that the higher systems have<br />

even greater power – they can solve a problem that is too hard to bel<strong>on</strong>g to any<br />

class in the hierarchy [GS12].<br />

References<br />

[CP04] C. S. Calude and Gh. Păun. Bio-steps bey<strong>on</strong>d Turing. BioSystems, 77:175–<br />

194, 2004.<br />

[EN02] G. Etesi and I. Németi. N<strong>on</strong>-Turing computati<strong>on</strong>s via Malament-Hogarth<br />

space-times. <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> Journal of Theoretical Physics, 41:341–370, 2002.<br />

arXiv:gr-qc/0104023v2.<br />

[G + 09] S. Gillessen et al. M<strong>on</strong>itoring stellar orbits around the Massive Black Hole in<br />

the Galactic Center. The Astrophysical Journal, 692:1075–1109, 23 February<br />

2009.<br />

[GS12] M. Gheorghe and M. Stannett. <strong>Membrane</strong> system models for super-Turing<br />

paradigms. Natural <strong>Computing</strong>, 11:253–259, 2012.<br />

[Hog04] M. Hogarth. Deciding Arithmetic using SAD Computers. The British Journal<br />

for the Philosophy of Science, 55:681–691, 2004.<br />

[NC00] M. Nielsen and I. Chuang. Quantum Computati<strong>on</strong> and Quantum Informati<strong>on</strong>.<br />

Cambridge University Press, Cambridge, 2000.<br />

[Pău11] Gh. Păun. <strong>Membrane</strong> <strong>Computing</strong> at Twelve Years (Back to Turku). In Proc.<br />

UC 2011, volume 6714 of LNCS, pages 36–37. Springer, 2011.<br />

[Pău12] Gh. Păun. Fypercomputati<strong>on</strong>s. In Marian Gheorghe, Gheorghe Păun, and<br />

Mario J. Pérez-Jiménez, editors, Fr<strong>on</strong>tiers of <strong>Membrane</strong> <strong>Computing</strong>: Open<br />

Problems and Research Topics, pages 207–209, to appear, 2012. http://www.<br />

gcn.us.es/10BWMC/10BWMCvolI/papers/megaPfinal.pdf.<br />

[Sho97] P. W. Shor. Polynomial-Time Algorithms for Prime Factorizati<strong>on</strong> and Discrete<br />

Logarithms <strong>on</strong> a Quantum Computer. SIAM J. Comput., 26(5):1484–<br />

1509, 1997.<br />

[Tho54] J. F. Thoms<strong>on</strong>. Tasks and Super-Tasks. Analysis, 15(1):1–13, October 1954.<br />

65

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