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13th International Conference on Membrane Computing - MTA Sztaki

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B. Aman, G. Ciobanu<br />

to reiterate the entire process. Applying CPN Tools <strong>on</strong> this extended system, we<br />

obtain the following output file:<br />

Home Markings: All<br />

Dead Markings: N<strong>on</strong>e;<br />

Dead Transiti<strong>on</strong> Instances: N<strong>on</strong>e Live Transiti<strong>on</strong> Instances: All<br />

Fairness Properties: All,<br />

meaning that from any reachable c<strong>on</strong>figurati<strong>on</strong> M i we can always reach any<br />

c<strong>on</strong>figurati<strong>on</strong> M j (home marking), the computati<strong>on</strong> never stops (dead marking),<br />

and so there are infinite occurrence sequences.<br />

7 C<strong>on</strong>clusi<strong>on</strong><br />

In this paper we c<strong>on</strong>tinue the research line started in [4], and present a new<br />

c<strong>on</strong>necti<strong>on</strong> between the systems of mobile membranes and colored Petri nets.<br />

The novelty of this formal translati<strong>on</strong>, with respect to the <strong>on</strong>e presented in [4],<br />

is that the number of membranes in the system could change during evoluti<strong>on</strong>.<br />

The systems of mobile membranes with objects <strong>on</strong> surface used in this translati<strong>on</strong><br />

are bounded to a given number of membranes.<br />

The structure of the parallel computati<strong>on</strong>s of the mobile membranes is faithfully<br />

reflected by the parallel semantics of the corresp<strong>on</strong>ding colored Petri nets.<br />

In mobile membranes, the parallel way of using the rules means that in each<br />

step we apply a maximal set of rules, namely a set of rules such that no further<br />

rule can be added to this set. Since we deal with mobility, each object and each<br />

membrane can be used <strong>on</strong>ly <strong>on</strong>ce in the rules applied in a step.<br />

We have c<strong>on</strong>sidered the low-density lipoprotein degradati<strong>on</strong> pathway, and<br />

described this biological process by using the mobile membranes with objects<br />

<strong>on</strong> membranes. The translati<strong>on</strong> of mobile membranes into colored Petri nets<br />

allows to obtain a descripti<strong>on</strong> of the biological process into colored Petri net, and<br />

then use a software called CPN Tools in analyzing several behavioral properties:<br />

reachability, boundedness, liveness, fairness. By encoding biological systems in<br />

this way, many interesting biological questi<strong>on</strong>s can get precise answers. Using<br />

CPN Tools, several (potentially infinite) behaviors can be investigated, a fact<br />

that is interesting from a biological point of view. Finally, we have provided a<br />

new link between biology, membrane systems and Petri nets which is, hopefully,<br />

useful for all these areas.<br />

Acknowledgements<br />

The work was supported by a grant of the Romanian Nati<strong>on</strong>al Authority for Scientific<br />

Research CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0919.<br />

The work of Bogdan Aman was also supported by POSDRU/89/1.5/S/49944.<br />

References<br />

1. B. Aman, G. Ciobanu. Mobility in Process Calculi and Natural <strong>Computing</strong>.<br />

Springer, 2011.<br />

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