13th International Conference on Membrane Computing - MTA Sztaki

H. ElGindy, R. Nicolescu, H. Wu
terminates after all cells enter a final state. Pseudocode 8 shows how ruleset R
is applied.
Pseudocode 8: Matrix structured ruleset application
1 Input : a P module, Π = (V, E, Q, O, R)
2 R = (R 1, . . . R m), 1 ≤ m, and R i = (R i,1, . . . , R i,mi ), 1 ≤ m i
3 applied = f a l s e
4 for i = 1 to m
5 for j = 1 to m i
6 i f R i,j is applicable then
7 apply R i,j: “here” symbols become immediately available
8 outgoing messages are queued
9 applied = true
10 endif
11 endfor
12 i f applied then
13 send all queued messages
14 break
15 endif
16 endfor
For example, consider the following vector, R 1 = (R 1,1 , R 1,2 , R 1,3 ), in a system
where cell σ 1 contains one symbol, a, and has one child cell, σ 2 .
R 1,1 : S 0 a → min S 0 c (f)↓ 2
R 1,2 : S 0 b → min S 1 d (g)↓ 2
R 1,3 : S 0 c → min S 0 e (h)↕ 2
For σ 1 , this vector is applied in one step. First, rule R 1,1 is applied: one c
becomes immediately available and message f is queued for transfer to σ 2 . Next,
the lower-priority rule R 1,2 is not applicable, for two distinct reasons: (1) there
is no b in the current contents and (2) it indicates a target state, S 1 , different
from the one already selected, S 0 .
Finally, rule R 1,3 is applied: one e becomes available and message h is further
queued for transfer to σ 2 . At the end of the step, σ 1 contains one e and the queued
symbols, f and h, are transferred to σ 2 .
Complex symbols: While atomic symbols seem sufficient for many theoretical
studies (such as computational completeness), complex algorithms need
adequate complex data structures. We enhance our initial vocabulary, by recursive
composition of elementary symbols from O into complex symbols, which
are compound terms of the form: t(i, . . . ), where (1) t is an elementary symbol
representing the functor; (2) i can be (a) an elementary symbol, (b) another
complex symbol, (c) a free variable (open to be bound, according to the cell’s
current configuration), (d) a multiset of elementary and complex symbols and
free variables.
We often abbreviate complex symbols by using subscripts for term arguments.
The following are examples of complex symbols, where a, b, c, d, e, f are
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