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13th International Conference on Membrane Computing - MTA Sztaki

13th International Conference on Membrane Computing - MTA Sztaki

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Using a kernel P system to solve the 3-Col problem<br />

green or red, then, in the next kP system c<strong>on</strong>figurati<strong>on</strong>, the S symbol from<br />

this membrane will disappear.<br />

The properties expressed before were checked for several kP systems, having<br />

different graph structures, which implied obtaining different results for these<br />

formulas, true or false plus a corresp<strong>on</strong>ding counterexample. For higher values<br />

of n the kP system simulati<strong>on</strong> is realised in a few sec<strong>on</strong>ds, but the property<br />

verificati<strong>on</strong> faces the well-known ‘state explosi<strong>on</strong> problem’.<br />

6 C<strong>on</strong>clusi<strong>on</strong>s<br />

Kernel P systems offer an unitary and elegant way of integrating established<br />

features of existing P system variants with new elements, valuable for formal<br />

modelling. This paper presents a case study illustrating the expressive power<br />

and efficiency of kernel P systems <strong>on</strong> the 3-Col problem. It presents a kP system<br />

that models the problem and compares it with a tissue P system model available<br />

in the literature; the comparis<strong>on</strong> proves the efficiency and expressiveness of kP<br />

systems. The paper also makes a first step towards formal verificati<strong>on</strong> of kP<br />

systems: the kP system model for the 3-Col problem is implemented in Promela<br />

and a number of rules for c<strong>on</strong>verting a kP system into a Promela implementati<strong>on</strong><br />

are identified. Furthermore, using this implementati<strong>on</strong>, a number of interesting<br />

properties are formally verified using Spin.<br />

In future work we will c<strong>on</strong>tinue to asses the modelling power and efficiency<br />

of kP systems in other case studies. Another priority is the development of a<br />

platform for simulati<strong>on</strong> and formal verificati<strong>on</strong> of kP systems.<br />

Acknowledgement. The work of FI and RL was supported by a grant of<br />

the Romanian Nati<strong>on</strong>al Authority for Scientific Research, CNCS–UEFISCDI,<br />

project number PN-II-ID-PCE-2011-3-0688. The author MPJ acknowledges the<br />

support of the project TIN2009–13192 of the Ministerio de Ciencia e Innovación<br />

of Spain, cofinanced by FEDER funds, and the support of the Project of Excellence<br />

with Investigador de Rec<strong>on</strong>ocida Valía of the Junta de Andalucía, grant<br />

P08–TIC–04200.<br />

References<br />

1. Ben-Ari, M.: Principles of the Spin Model Checker. Springer-Verlag, L<strong>on</strong>d<strong>on</strong> (2008)<br />

2. Ciobanu, G., Pérez-Jiménez, M.J., Păun, G. (eds.): Applicati<strong>on</strong>s of <strong>Membrane</strong><br />

<strong>Computing</strong>. Natural <strong>Computing</strong> Series, Springer (2006)<br />

3. Díaz-Pernil, D., Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Riscos-Núñez, A.:<br />

A uniform family of tissue P systems with cell divisi<strong>on</strong> solving 3-COL in a linear<br />

time. Theoretical Computer Science 404(1-2), 76–87 (2008)<br />

4. Díaz-Pernil, D., Pérez-Hurtado, I., Pérez-Jiménez, M.J., Riscos-Núñez, A.: A P-<br />

Lingua programming envir<strong>on</strong>ment for membrane computing. In: Corne, D.W.,<br />

Frisco, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) <strong>Membrane</strong> <strong>Computing</strong><br />

- 9th <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> Workshop, WMC 2008, Revised Selected and Invited Papers.<br />

Lecture Notes in Computer Science, vol. 5391, pp. 187–203. Springer (2009)<br />

255

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