13th International Conference on Membrane Computing - MTA Sztaki

DCBA: Simulating population dynamics P systems with proportional object
distribution
Algorithm 4 SELECTION PHASE 1: DISTRIBUTION
1: for j = 1 to m do ⊲ (For each environment e j)
2: Apply filters to table T j using C t, obtaining Tj t . The filters are applied as follows:
a. Tj t ← T j
b. Filter 1 (Tj t , C t).
c. Filter 2 (Tj t , C t).
d. Check mutual consistency for the blocks remaining in Tj t :
• Create a vector MCj, t of order q (number of membranes in Π), with
MCj(i) t = −1, 1 ≤ i ≤ q.
• for each column B i,α,α ′ ,u,v in Tj t , do
∗ if MCj(i) t = −1 then MCj(i) t ← α ′ .
∗ else if MCj(i) t = α ′ then do nothing.
∗ else store all the information about the inconsistency.
• if there was at least one inconsistency then report the information
about the error, and optionally halt the execution (in case of not
activating step 3.)
e. Filter 3 (Tj t , C t).
f. Tj,z t ← Tj
t
3: (OPTIONAL) Generate, from Tj t , sub-tables formed by sets of mutually
consistent blocks, in a maximal way in Tj
t (by the inclusion relationship). This
will produce a set of sub-tables Tj,k, t k = 1, . . . , s. Randomly select one table from
the set: Tj,z
t
4: a ← 1
5: Ct a ← C t
′
6: repeat
7: Add up the values of each row in Tj,z. t Filter the rows whose sum is 0.
8: Each element of the table is divided by the sum of the values from the
corresponding row.
9: For each pair (o, i) and (x, e) ∈ Ct a , if the object in Ct a has multiplicity
mult > 0, all the elements of the corresponding row in Tj,z t are multiplied by mult,
by the corresponding value in Tj,z
t (computed in the previous step), and by the
original value in T j. That is, if in the position (X, Y ) of the table T j there is a not
null value, and the corresponding object in the row X has multiplicity mult X,a,t
in Ct a , then:
T t j,z(X, Y ) = ⌊mult X,a,t · T t j,z(X, Y ) ·
Tj,z(X, t Y )
⌋ = ⌊mult X,a,t · (T j,z(X, t Y )) 2
⌋
RowSum X,t RowSum X,t
10: For each block B (i.e., column) appearing (i.e. not filtered) in Tj,z, t calculate
the minimum number of the previously calculated values, NB
a ≥ 0. This is the
number of times the block is going to be applied. This value is accumulated to the
total calculated through the iteration of the loop over a: B j sel
← B j sel
+ {B N B a }
11: C a+1
t ← Ct a − LHS(B) · NB a ⊲ (Delete the LHS of the block.)
12: Filter 2 (Tj,z, t C a+1
t )
13: Filter 3 (Tj,z, t C a+1
t )
14: a ← a + 1
15: until (a > A) ∨ (all the selected minimums in step 10 are 0)
16: end for
299