13th International Conference on Membrane Computing - MTA Sztaki

A. Ţurcanu, F. Ipate
act1 : cell : |((∀s, j.s ∈ SY MBOLS&j ∈ 1 ...n&j ≠ i ⇒
cell ′ (y)(s)(j) =cell(x)(s)(j))&(cell ′ (y)(a)(i) =cell(x)(a)(i) − 1)
&(cell ′ (y)(r)(i) =cell(x)(r)(i)+1)&(∀s.s ∈ SY MBOLS \{a, r}
&cell ′ (y)(s)(i) =cell(x)(s)(i))&(∀s, j.s ∈ SY MBOLS&j ∈ 1 ...n
&i ≠ j ⇒ cell ′ (z)(s)(j) =cell(x)(s)(j))&
(cell ′ (z)(a)(i) =cell(x)(a)(i) − 1)&(cell ′ (z)(t)(i) =cell(x)(t)(i)+1)
&(∀s.s ∈ SY MBOLS \{a, t}&cell ′ (z)(s)(i) =cell(x)(s)(i))&
(∀w, s, j.w ∈ dom(cell)&w ≠ x&s ∈ SY MBOLS&j ∈ 1 ...n
⇒ cell ′ (w)(s)(j) =cell(w)(s)(j)))
act2 : mark := ({x} ✁−mark) ∪{y ↦→ 1,z ↦→ 1}
Therefore, the rule is applied in some random cell x, for some random value
of the index i and it modifies accordingly the values of the function cell. Two
new cells, y and z, are replacing x in the membrane structure of the system as
a result of the division. Any other cell w is not affected by the rule.
In [3] we verified some properties of Π(n) with the model checker ProB using
this general model, instantiated for particular values of n.
Using similar ideas and possibly renaming objects and using indices, we can
build Event-B models of various P systems with active membranes.
4 Conclusions and Future Work
Based on rigorous mathematical foundation and allowing high-level modelling,
Event-B and Rodin offer a simpler and more convenient way of modelling P
systems by using quantifiers, non-deterministic assignments and functions. In
this paper we have presented some general ideas about this way of modelling.
Our future work will concentrate on generalising and automating this method
of modelling in Event-B for different types of P systems.
References
[1] Abrial, J.R., Modeling in Event-B. System and software engineering, Cambridge
University Press, (2010)
[2] Díaz-Pernil, D., Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Riscos-
Núñez, A.: A linear-time tissue P system based solution for the 3-coloring
problem. Electr. Notes Theor. Comput. Sci. 171(2), 81-93 (2007)
[3] Lefticaru, R., Ipate, F., Cabrera, L. V., Ţurcanu, A., Tudose, C., Gheorghe,
M. Pérez-Jiménez, M., Niculescu, I. M., Dragomir, C.: Towards an integrated
approach for model simulation, property extraction and verification
of P systems. In: Proceedings of 10th BWMC, pp. 291–318 (2012)
[4] Păun, G.: Computing with membranes. Journal of Computer and System
Sciences 61(1), 108–143 (2000)
[5] Ţurcanu, A., Ipate, F.: Modelling, testing and verification of P systems
with active membranes using Rodin and ProB modelling. In: Proceedings
of the 12th <strong>International</strong> <strong>Conference</strong> on Membrane Computing. pp. 459-
468. Paris-Est University Press (2011)
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