13th International Conference on Membrane Computing - MTA Sztaki

DCBA: Simulating population dynamics P systems with proportional object
distribution
Algorithm 3 INITIALIZATION
1: Construction of the static distribution table T :
– Column labels: consistent blocks of rules from R: B i,α,α ′ ,u,v
– Row labels: pairs (o, i) and (o ′ , e), for all object o ∈ Γ , o ′ ∈ Σ and membrane
i, e being a generic identifier of the environments of the P system.
– For each consistent block B, each object o ∈ Γ and i, place at row labelled
by (o, i) and column labelled by B the fraction 1 if o appears within i with
k
multiplicity k in the LHS of B, or place a null value otherwise; do the same for
each object x ∈ Σ appearing outside the skin membrane (i.e. the environment).
2: for j = 1 to m do ⊲ (Construct the expanded table T j)
3: T j ← T . ⊲ (Initialize the table with the original T )
4: For each communication rule block B from R E, which is associated with the
environment e j, add a column labelled by B to the table T j; place the value 1 at
row (x, e) and column B, x being the object appearing in the LHS of B.
5: end for
6: Initialize the multisets B j sel
← ∅ and R j sel ← ∅
called static table, is used in each time step, so it is initialized only once, at the
beginning of the algorithm. The static table has one column per each consistent
block of rules, and one row per each pair of object and compartment (i.e., each
membrane and the environment). An expanded static table T j is also constructed
for each environment, to consider also blocks from environment communication
rules. Finally, for each environment, two multisets B j sel and Rj sel
, are initialized.
They are used by the algorithm in order to store the selected blocks and the
selected rules, respectively.
The distribution of objects among the blocks with overlapping LHS is
performed in Selection Phase 1 (Algorithm 4). The expanded static table T j
is used for this purpose in each environment. Three filters are defined in order
to adapt T j to the configuration C t of the system; that is, to select which
blocks are going to receive objects. Filter 1 discards the columns of the table
corresponding to non-applicable blocks due to mismatch charges in the LHS.
Filter 2 discards the columns corresponding to non-applicable blocks due to
the objects from the LHS. The goal of Filter 3 is to save space in the table,
discarding rows that become empty because of the previous filters. These three
filters are applied at the beginning of phase 1, and the result is a dynamic table
Tj t (for the environment j and time step t).
Filter procedures for selection Phase 1
procedure Filter 1(table T , configuration C) ⊲ (By columns and charges)
Discard columns from table T , according to the charge of the membrane in the
LHS of the corresponding block and in the configuration C.
end procedure
procedure Filter 2(table T , configuration C) ⊲ (By columns and multiplicity)
Discard columns from table T , such that for any row (o, i) or (x, e), the
multiplicity of that object in C multiplied by 1/k (the value in the table), returns a
number κ, 0 ≤ κ < 1. If all the values for that column are null, it is also filtered.
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