13th International Conference on Membrane Computing - MTA Sztaki

Observer/interpreter P systems
there might be the case when Π, being in configuration C ′ , it also executes rules
of type ca r → cX r . In this case, the finite state machine M cannot pass from
state l 1 to l 2 or l 3 and the input is rejected.
Without any loss of generality, let us consider that the current register machine
instruction to be executed is l 1 : (sub(r 1 ), l 2 , l 3 ) (that is M atempts to
decrement register 1) and that Π is in a configuration C = l 1 a k1
1 ak2 2 ak3 3 , with
k 1 , k 2 , k 3 ≥ 0. We have two possible cases:
Case 1: k 1 ≥ 1. In this case Π executes the rule a 1 → a 1 (if in the current
multiset there are also the objects a 2 and a 3 , then also the rules a 2 → a 2 and
a 3 → a 3 are executed) and one of the rules l 1 → l 2 or l 1 → l 3 . If the rule
l 1 → l 2 is executed, then M passes from state l 1 to l 2 , otherwise M halts in
state l 1 rejecting the computation. Next, if M is in state l 2 and the system
Π is in configuration l 2 a k1
1 ak2 2 ak3 3 the rules that can be applied are: l 2 → l 2 ,
a r → a r , and ca r → CX r , for 1 ≤ r ≤ 3 (from these rules only the rule l 2 → l 2
will surely be applied, while the others will be applied, depending on the values
of k 1 , k 2 , and k 3 , in any combination but such that at least one of the rules
a r → a r and ca r → CX r , 1 ≤ r ≤ 3, will be selected for application; moreover
if a rule involving the catalyst c is applied, then all the other rules involving c
are not applied). Consequently M can pass from state l 2 to state l 2 if and only
if ca 1 → cX 1 is applied (that is, X 1 ↑ appears in the observation set).
Case 2: k 1 = 0. In this situation, Π cannot execute the rule a 1 → a 1 because
there is no object a 1 , hence the number of objects a 1 remains unchanged. It
follows that M goes from state l 1 to state l 3 if the rule l 1 → l 3 is executed (the
observation set is {a 1 −, l 1 ↓, l 3 ↑}). Next, M will pass from state l 3 to state l 3
iff the rules ca 2 → cX 2 and ca 3 → cX 3 are not applied (that is, if there exist
the objects a 2 and a 3 , then only the rules a 2 → a 2 and a 3 → a 3 are applied).
Assuming now that M is in the state labeled l h and the object with the same
name l h is generated by Π, then M changes its state to l H iff the rules l h → λ
and a i → a i , 1 ≤ i ≤ 3, are applied (the observation set {l h ↓, a 1 −, a 2 −, a 3 −}
guarantees that the rules a i → a i are not applied because the number of objects
a i remains constant between the two consecutive configurations). Hence, the
computations of Π and M halt and the generated set is the content of register
r.
4 Conclusions and Further Work
In this paper we have introduced and studied Observer/Interpreter P systems
which were motivated by the possibility of tracking and detecting genetically
encoded fluorescent proteins in living cells. Their discovery produced a major
development in the live imaging of cells. In this respect, intracellular dynamics
was able to be monitored and studied. Moreover, the discovery of these proteins
allowed the creation of specific biosensors which were further used to monitor a
wide range of intracellular phenomena (like apoptosis, pH and metal-ion concentration,
protein kinase activity, membrane voltage, cyclic nucleotide signaling,
and so on).
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