13th International Conference on Membrane Computing - MTA Sztaki

A.E. Porreca, A. Leporati, G. Mauri, C. Zandron
When membranes i j revert to neutral, the input objects a i are sent back in,
all the way to the input membrane h 0 :
a i [ ] 0 i j
→ [a i ] 0 i j
(13)
These rules are replicated for all 0 ≤ i < n, 0 ≤ j < l(n), a ∈ Σ.
Once again, the state object waits n 2
+ l(n) + 1 steps (this time, inside membrane
h) for this process to complete:
[qi,w t → q t+1
i,w ]0 h for 0 ≤ t < n + l(n) + 1 (14)
2
These rules are replicated for all q ∈ Q, 0 ≤ i < n, 0 ≤ w < s(n).
Next, the state object q n i,w enters membrane w w and changes its charge, thus
causing the object a inside it to be sent out.
qi,w n [ ] 0 w w
→ [q i,w] ′′ w w
(15)
[a] + w w
→ [ ] − w w
a (16)
These rules are replicated for all q ∈ Q, 0 ≤ i < n, 0 ≤ w < s(n), a ∈ Σ.
When the charge of w w becomes negative, the state object is sent out to
h, while object a enters the corresponding membrane a w and sets its charge to
positive.
[q ′′
i,w] − w w
→ [ ] − w w
q ′′
i,w (17)
a [ ] 0 a w
→ [a] + a w
(18)
These rules are replicated for all q ∈ Q, 0 ≤ i < n, 0 ≤ w < s(n), a ∈ Σ.
Now the conguration of Π x (see Fig. 4) has the following properties:
Exactly one membrane among w 0 , . . . , w s(n)−1 is negatively charged (this is
the membrane corresponding to the work tape cell currently scanned by M)
while the others are neutral.
Exactly one membrane a i is positively charged (the one corresponding to
the input tape symbol currently read by M), while b i is neutral for all
b ∈ Σ − {a}.
Exactly one membrane a w is positively charged (the one corresponding to the
work tape symbol currently read by M), while b w is neutral for all b ∈ Σ−{a}.
While the object a inside membrane a w
replicated for all a ∈ Σ:
is deleted by the following rule,
[a → λ] + a w
(19)
the state object can identify the symbols currently read by M by checking the
charges of the corresponding membranes (resetting them to neutral), and store
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